Method and system for determining treatments by modifying patient-specific geometrical models

ABSTRACT

Systems and methods are disclosed for evaluating cardiovascular treatment options for a patient. One method includes creating a three-dimensional model representing a portion of the patient&#39;s heart based on patient-specific data regarding a geometry of the patient&#39;s heart or vasculature; and for a plurality of treatment options for the patient&#39;s heart or vasculature, modifying at least one of the three-dimensional model and a reduced order model based on the three-dimensional model. The method also includes determining, for each of the plurality of treatment options, a value of a blood flow characteristic, by solving at least one of the modified three-dimensional model and the modified reduced order model; and identifying one of the plurality of treatment options that solves a function of at least one of: the determined blood flow characteristics of the patient&#39;s heart or vasculature, and one or more costs of each of the plurality of treatment options.

TECHNICAL FIELD

Embodiments include methods and systems for determining patienttreatment options, and more particularly, to methods and systems fordetermining treatment options by modifying patient-specific geometricmodels.

BACKGROUND

Coronary artery disease may produce coronary lesions in the bloodvessels providing blood to the heart, such as a stenosis (abnormalnarrowing of a blood vessel). As a result, blood flow to the heart maybe restricted. A patient suffering from coronary artery disease mayexperience chest pain, referred to as chronic stable angina duringphysical exertion or unstable angina when the patient is at rest. A moresevere manifestation of disease may lead to myocardial infarction, orheart attack.

A need exists to provide more accurate data relating to coronarylesions, e.g., size, shape, location, functional significance (e.g.,whether the lesion impacts blood flow), etc. Patients suffering fromchest pain and/or exhibiting symptoms of coronary artery disease may besubjected to one or more tests that may provide some indirect evidencerelating to coronary lesions. For example, noninvasive tests may includeelectrocardiograms, biomarker evaluation from blood tests, treadmilltests, echocardiography, single positron emission computed tomography(SPECT), and positron emission tomography (PET). These noninvasivetests, however, typically do not provide a direct assessment of coronarylesions or assess blood flow rates. The noninvasive tests may provideindirect evidence of coronary lesions by looking for changes inelectrical activity of the heart (e.g., using electrocardiography(ECG)), motion of the myocardium (e.g., using stress echocardiography),perfusion of the myocardium (e.g., using PET or SPECT), or metabolicchanges (e.g., using biomarkers).

For example, anatomic data may be obtained noninvasively using coronarycomputed tomographic angiography (CCTA). CCTA may be used for imaging ofpatients with chest pain and involves using computed tomography (CT)technology to image the heart and the coronary arteries following anintravenous infusion of a contrast agent. However, CCTA also cannotprovide direct information on the functional significance of coronarylesions, e.g., whether the lesions affect blood flow. In addition, sinceCCTA is purely a diagnostic test, it cannot be used to predict changesin coronary blood flow, pressure, or myocardial perfusion under otherphysiologic states, e.g., exercise, nor can it be used to predictoutcomes of interventions.

Thus, patients may also require an invasive test, such as diagnosticcardiac catheterization, to visualize coronary lesions. Diagnosticcardiac catheterization may include performing conventional coronaryangiography (CCA) to gather anatomic data on coronary lesions byproviding a doctor with an image of the size and shape of the arteries.CCA, however, does not provide data for assessing the functionalsignificance of coronary lesions. For example, a doctor may not be ableto diagnose whether a coronary lesion is harmful without determiningwhether the lesion is functionally significant. Thus, CCA has led towhat has been referred to as an “oculostenotic reflex” of someinterventional cardiologists to insert a stent for every lesion foundwith CCA regardless of whether the lesion is functionally significant.As a result, CCA may lead to unnecessary operations on the patient,which may pose added risks to patients and may result in unnecessaryheath care costs for patients.

During diagnostic cardiac catheterization, the functional significanceof a coronary lesion may be assessed invasively by measuring thefractional flow reserve (FFR) of an observed lesion. FFR is defined asthe ratio of the mean blood pressure downstream of a lesion divided bythe mean blood pressure upstream from the lesion, e.g., the aorticpressure, under conditions of increased coronary blood flow, e.g.,induced by intravenous administration of adenosine. The blood pressuresmay be measured by inserting a pressure wire into the patient. Thus, thedecision to treat a lesion based on the determined FFR may be made afterthe initial cost and risk of diagnostic cardiac catheterization hasalready been incurred.

Thus, a need exists for a method for assessing coronary anatomy,myocardial perfusion, and coronary artery flow noninvasively. Such amethod and system may benefit cardiologists who diagnose and plantreatments for patients with suspected coronary artery disease. Inaddition, a need exists for a method to predict coronary artery flow andmyocardial perfusion under conditions that cannot be directly measured,e.g., exercise, and to predict outcomes of medical, interventional, andsurgical treatments on coronary artery blood flow and myocardialperfusion.

In addition, a need exists to automatically identify an optimaltreatment option from a plurality of feasible treatment options (e.g.,all possible percutaneous coronary intervention (PCI) or coronaryarterial bypass grafts (CABG) options), by analyzing noninvasivelyassessed coronary anatomy.

SUMMARY OF THE DISCLOSURE

In certain embodiments, systems are disclosed for evaluatingcardiovascular treatment options for a patient. A system includes atleast one computer system configured to: create a three-dimensionalmodel representing at least a portion of the patient's heart orvasculature based on patient-specific data regarding a geometry of thepatient's heart or vasculature; and for each of a plurality of treatmentoptions for treating at least a portion of the patient's heart orvasculature, modify at least one of the three-dimensional model and areduced order model based on the three-dimensional. The computer systemis further configured to determine, for each of the plurality oftreatment options, a value of a blood flow characteristic, by solving atleast one of the modified three-dimensional model and the modifiedreduced order model; and identify one of the plurality of treatmentoptions that solves a function of at least one of: the determined bloodflow characteristics of the patient's heart or vasculature, and one ormore costs of each of the plurality of treatment options.

In certain embodiments, the computer system is configured to modify, foreach of the plurality of treatment options, the three-dimensional modelusing a geometric modification technique. The computer system isconfigured to modify, for each of the plurality of treatment options,the three-dimensional model using a constructive solid geometry union.The computer system is configured to modify, for each of the pluralityof treatment options, the three-dimensional model using an elasticdeformation modification technique. The computer system is configured tomodify, for each of the plurality of treatment options, thethree-dimensional model based on a simulated location of an insertedstent or bypass graft. The computer system is configured to modify thethree-dimensional model for a subset of each of the plurality oftreatment options in locations that exhibit a predetermined thresholdlevel of a blood flow characteristic.

In certain embodiments, the computer system is configured to: create thereduced order model relating to a blood flow characteristic of thepatient's heart or vasculature, based on the three-dimensional model;and modify the reduced order model for each possible treatment option,using a resistance value estimated to be associated with a type andlocation of the respective possible treatment option. The computersystem is configured to determine resistance values associated withpossible treatment options from historical data of known resistancevalues associated with a known dimension or geometry of previouslyimplemented treatment options. The objective function is configured tomaximize blood flow or minimize pressure changes in a patient's coronaryvasculature. The objective function is configured to penalize one ormore of: increasing numbers of stents or bypass grafts; decreasing ofFFR values in larger vessels, as opposed to smaller vessels; increasingproximity of inserted stents; treatment costs; and the existence ornumber of bifurcations. The three-dimensional model representing atleast the portion of the patient's heart includes at least a portion ofan aorta and at least a portion of a plurality of coronary arteriesemanating from the portion of the aorta.

In certain embodiments, the blood flow characteristic indicates a ratiobetween a pressure in the aorta and a pressure at a location in theplurality of coronary arteries; and the computer system is configured todetermine the blood flow characteristic at a plurality of locations inthe plurality of coronary arteries. The patient-specific data includesimaging data provided by computer tomography or magnetic resonanceimaging techniques. The reduced order model includes at least one lumpedparameter model representing a blood flow through boundaries of thethree-dimensional model. The computer system is configured to determinethe blood flow characteristic using a parameter associated with at leastone of a level of hyperemia, a level of exercise, or a medication.

In certain embodiments, methods are disclosed for evaluatingcardiovascular treatment options for a patient. One method includescreating a three-dimensional model representing at least a portion ofthe patient's heart or vasculature based on patient-specific dataregarding a geometry of the patient's heart or vasculature; and for eachof a plurality of treatment options for treating at least a portion ofthe patient's heart or vasculature, modifying at least one of thethree-dimensional model and a reduced order model based on thethree-dimensional model. The method also includes determining, for eachof the plurality of treatment options, a value of a blood flowcharacteristic, by solving at least one of the modifiedthree-dimensional model and the modified reduced order model; andidentifying one of the plurality of treatment options that solves afunction of at least one of: the determined blood flow characteristicsof the patient's heart or vasculature, and one or more costs of each ofthe plurality of treatment options.

In certain embodiments, the method includes modifying, for each of theplurality of treatment options, the three-dimensional model using atleast one of: a geometric modification technique; a constructive solidgeometry union; and an elastic deformation modification technique. Themethod further includes modifying, for each of the plurality oftreatment options, the three-dimensional model based on a simulatedlocation of an inserted stent or bypass graft. The method furtherincludes modifying the three-dimensional model for a subset of each ofthe plurality of treatment options in locations that exhibit apredetermined threshold level of a blood flow characteristic.

The method further includes creating the reduced order model relating toa blood flow characteristic of the patient's heart or vasculature, basedon the three-dimensional model; and modifying the reduced order modelfor each possible treatment option, using a resistance value estimatedto be associated with a type and location of the respective possibletreatment option. The method further includes determining resistancevalues associated with possible treatment options from historical dataof known resistance values associated with a known dimension or geometryof previously implemented treatment options.

The objective function is configured to maximize blood flow or minimizepressure changes in a patient's coronary vasculature. The objectivefunction is configured to penalize one or more of: increasing numbers ofstents or bypass grafts; decreasing of FFR values in larger vessels, asopposed to smaller vessels; increasing proximity of inserted stents;treatment costs; and the existence or number of bifurcations. thethree-dimensional model representing at least the portion of thepatient's heart includes at least a portion of an aorta and at least aportion of a plurality of coronary arteries emanating from the portionof the aorta. The blood flow characteristic indicates a ratio between apressure in the aorta and a pressure at a location in the plurality ofcoronary arteries; and the computer system is configured to determinethe blood flow characteristic at a plurality of locations in theplurality of coronary arteries.

The patient-specific data includes imaging data provided by computertomography or magnetic resonance imaging techniques. The reduced ordermodel includes at least one lumped parameter model representing a bloodflow through boundaries of the three-dimensional model. The methodfurther includes determining the blood flow characteristic using aparameter associated with at least one of a level of hyperemia, a levelof exercise, or a medication.

The foregoing general description and the following detailed descriptionare exemplary and explanatory only and are not restrictive of thedisclosure.

Additional embodiments and advantages will be set forth in part in thedescription which follows, and in part will be obvious from thedescription, or may be learned by practice of the disclosure. Theembodiments and advantages will be realized and attained by means of theelements and combinations particularly pointed out below.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate several embodiments and togetherwith the description, serve to explain the principles of the disclosure.

FIG. 1 is a schematic diagram of a system for providing variousinformation relating to coronary blood flow in a specific patient,according to an exemplary embodiment;

FIG. 2 is a flow chart of a method for providing various informationrelating to blood flow in a specific patient, according to an exemplaryembodiment;

FIG. 3 is a flow chart showing the substeps of the method of FIG. 2;

FIG. 4 shows imaging data obtained noninvasively from a patient,according to an exemplary embodiment;

FIG. 5 shows an exemplary three-dimensional model generated using theimaging data of FIG. 4;

FIG. 6 shows a portion of a slice of the imaging data of FIG. 4including seeds for forming a first initial model;

FIG. 7 shows a portion of the first initial model formed by expandingthe seeds of FIG. 6;

FIG. 8 shows a trimmed solid model, according to an exemplaryembodiment;

FIG. 9 shows an exemplary computed FFR (cFFR) model when the patient isat rest;

FIG. 10 shows an exemplary cFFR model when the patient is under maximumhyperemia;

FIG. 11 shows an exemplary cFFR model when the patient is under maximumexercise;

FIG. 12 shows a portion of a trimmed solid model provided for forming alumped parameter model, according to an exemplary embodiment;

FIG. 13 shows a portion of the centerlines for the trimmed solid modelof FIG. 12, provided for forming a lumped parameter model;

FIG. 14 shows segments formed based on the trimmed solid model of FIG.12, provided for forming a lumped parameter model;

FIG. 15 shows the segments of FIG. 14 replaced by resistors, providedfor forming a lumped parameter model;

FIG. 16 shows exemplary lumped parameter models representing theupstream and downstream structures at the inflow and outflow boundariesof a solid model, according to an exemplary embodiment;

FIG. 17 shows a three-dimensional mesh prepared based on the solid modelof FIG. 8;

FIGS. 18 and 19 show portions of the three-dimensional mesh of FIG. 17;

FIG. 20 shows a model of the patient's anatomy including blood flowinformation with certain points on the model identified by individualreference labels;

FIG. 21 is a graph of simulated blood pressure over time in the aortaand at some of the points identified in FIG. 20;

FIG. 22 is a graph of simulated blood flow over time at each of thepoints identified in FIG. 20;

FIG. 23 is a finalized report, according to an exemplary embodiment;

FIG. 24 is a flow chart of a method for providing various informationrelating to coronary blood flow in a specific patient, according to anexemplary embodiment;

FIG. 25 shows a modified cFFR model determined based on a solid modelcreated by widening a portion of the left anterior descending (LAD)artery and a portion of the LCX artery, according to an exemplaryembodiment;

FIG. 26 shows an example of a modified simulated blood flow model afterwidening a portion of the LAD artery and a portion of the leftcircumflex (LCX) artery, according to an exemplary embodiment;

FIG. 27 is a flow chart of a method for simulating various treatmentoptions using a reduced order model, according to an exemplaryembodiment;

FIG. 28 is a flow chart of a method for simulating various treatmentoptions using a reduced order model, according to another exemplaryembodiment;

FIG. 29 is a flow chart of a method for determining an optimal treatmentoption by modifying a patient-specific geometric model;

FIG. 30 depicts an exemplary embodiment of a method of a geometricdomain modification technique for modifying a patient-specific geometricmodel;

FIG. 31A depicts a diagram of a step of an exemplary method of ageometric domain modification technique for modifying a patient-specificgeometric model;

FIG. 31B depicts a diagram of another step of an exemplary method of ageometric domain modification technique for modifying a patient-specificgeometric model;

FIG. 32 depicts a graphical representation of a triangle mesh of anexemplary proposed stent geometry;

FIG. 33A depicts a graphical representation of a triangle mesh of anexemplary original patient geometry having a stenosis portion thatappears as a visible narrowing of a vessel;

FIG. 33B depicts a graphical representation of a triangle mesh resultingfrom a union between the exemplary original patient geometry meshdepicted in FIG. 33A and the exemplary stent mesh geometry depicted inFIG. 32; and

FIG. 34 depicts an exemplary method for performing an elasticdeformation technique for modifying a patient-specific geometric model.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to exemplary embodiments, examplesof which are illustrated in the accompanying drawings. Whereverpossible, the same reference numbers will be used throughout thedrawings to refer to the same or like parts. This description isorganized according to the following outline:

-   -   I. Overview    -   II. Obtaining and Preprocessing Patient-Specific Anatomical Data    -   III. Creating The Three-Dimensional Model Based On Obtained        Anatomical Data    -   IV. Preparing The Model For Analysis and Determining Boundary        Conditions        -   A. Preparing the Model For Analysis        -   B. Determining Boundary Conditions            -   i. Determining Reduced Order Models            -   ii. Exemplary Lumped Parameter Models        -   C. Creating the Three-Dimensional Mesh    -   V. Performing The Computational Analysis And Outputting Results        -   A. Performing the Computational Analysis        -   B. Displaying Results for Blood Pressure, Flow, and cFFR        -   C. Verifying Results        -   D. Another Embodiment of a System and Method for Providing            Coronary Blood Flow Information    -   VI. Providing Patient-Specific Treatment Planning        -   A. Using Reduced Order Models to Compare Different Treatment            Options        -   B. Modifying Patient-Specific Geometrical Models to Optimize

Treatment Options

I. Overview

In an exemplary embodiment, a method and system determines variousinformation relating to blood flow in a specific patient usinginformation retrieved from the patient noninvasively. The determinedinformation may relate to blood flow in the patient's coronaryvasculature. Alternatively, as will be described below in furtherdetail, the determined information may relate to blood flow in otherareas of the patient's vasculature, such as carotid, peripheral,abdominal, renal, and cerebral vasculature. The coronary vasculatureincludes a complex network of vessels ranging from large arteries toarterioles, capillaries, venules, veins, etc. The coronary vasculaturecirculates blood to and within the heart and includes an aorta 2 (FIG.5) that supplies blood to a plurality of main coronary arteries 4 (FIG.5) (e.g., the left anterior descending (LAD) artery, the left circumflex(LCX) artery, the right coronary (RCA) artery, etc.), which may furtherdivide into branches of arteries or other types of vessels downstreamfrom the aorta 2 and the main coronary arteries 4. Thus, the exemplarymethod and system may determine various information relating to bloodflow within the aorta, the main coronary arteries, and/or other coronaryarteries or vessels downstream from the main coronary arteries. Althoughthe aorta and coronary arteries (and the branches that extend therefrom)are discussed below, the disclosed method and system may also apply toother types of vessels.

In an exemplary embodiment, the information determined by the disclosedmethods and systems may include, but is not limited to, various bloodflow characteristics or parameters, such as blood flow velocity,pressure (or a ratio thereof), flow rate, and FFR at various locationsin the aorta, the main coronary arteries, and/or other coronary arteriesor vessels downstream from the main coronary arteries. This informationmay be used to determine whether a lesion is functionally significantand/or whether to treat the lesion. This information may be determinedusing information obtained noninvasively from the patient. As a result,the decision whether to treat a lesion may be made without the cost andrisk associated with invasive procedures.

FIG. 1 shows aspects of a system for providing various informationrelating to coronary blood flow in a specific patient, according to anexemplary embodiment. A three-dimensional model 10 of the patient'sanatomy may be created using data obtained noninvasively from thepatient as will be described below in more detail. Otherpatient-specific information may also be obtained noninvasively. In anexemplary embodiment, the portion of the patient's anatomy that isrepresented by the three-dimensional model 10 may include at least aportion of the aorta and a proximal portion of the main coronaryarteries (and the branches extending or emanating therefrom) connectedto the aorta.

Various physiological laws or relationships 20 relating to coronaryblood flow may be deduced, e.g., from experimental data as will bedescribed below in more detail. Using the three-dimensional anatomicalmodel 10 and the deduced physiological laws 20, a plurality of equations30 relating to coronary blood flow may be determined as will bedescribed below in more detail. For example, the equations 30 may bedetermined and solved using any numerical method, e.g., finitedifference, finite volume, spectral, lattice Boltzmann, particle-based,level set, finite element methods, etc. The equations 30 may be solvableto determine information (e.g., pressure, velocity, FFR, etc.) about thecoronary blood flow in the patient's anatomy at various points in theanatomy represented by the model 10.

The equations 30 may be solved using a computer 40. Based on the solvedequations, the computer 40 may output one or more images or simulationsindicating information relating to the blood flow in the patient'sanatomy represented by the model 10. For example, the image(s) mayinclude a simulated blood pressure model 50, a simulated blood flow orvelocity model 52, a computed FFR (cFFR) model 54, etc., as will bedescribed in further detail below. The simulated blood pressure model50, the simulated blood flow model 52, and the cFFR model 54 provideinformation regarding the respective pressure, velocity, and cFFR atvarious locations along three dimensions in the patient's anatomyrepresented by the model 10. cFFR may be calculated as the ratio of theblood pressure at a particular location in the model 10 divided by theblood pressure in the aorta, e.g., at the inflow boundary of the model10, under conditions of increased coronary blood flow, e.g.,conventionally induced by intravenous administration of adenosine.

In an exemplary embodiment, the computer 40 may include one or morenon-transitory computer-readable storage devices that store instructionsthat, when executed by a processor, computer system, etc., may performany of the actions described herein for providing various informationrelating to blood flow in the patient. The computer 40 may include adesktop or portable computer, a workstation, a server, a personaldigital assistant, or any other computer system. The computer 40 mayinclude a processor, a read-only memory (ROM), a random access memory(RAM), an input/output (I/O) adapter for connecting peripheral devices(e.g., an input device, output device, storage device, etc.), a userinterface adapter for connecting input devices such as a keyboard, amouse, a touch screen, a voice input, and/or other devices, acommunications adapter for connecting the computer 40 to a network, adisplay adapter for connecting the computer 40 to a display, etc. Forexample, the display may be used to display the three-dimensional model10 and/or any images generated by solving the equations 30, such as thesimulated blood pressure model 50, the simulated blood flow model 52,and/or the cFFR model 54.

FIG. 2 shows aspects of a method for providing various informationrelating to blood flow in a specific patient, according to anotherexemplary embodiment. The method may include obtaining patient-specificanatomical data, such as information regarding the patient's anatomy(e.g., at least a portion of the aorta and a proximal portion of themain coronary arteries (and the branches extending therefrom) connectedto the aorta), and preprocessing the data (step 100). Thepatient-specific anatomical data may be obtained noninvasively, e.g., byOCTA, as will be described below.

A three-dimensional model of the patient's anatomy may be created basedon the obtained anatomical data (step 200). For example, thethree-dimensional model may be the three-dimensional model 10 of thepatient's anatomy described above in connection with FIG. 1.

The three-dimensional model may be prepared for analysis and boundaryconditions may be determined (step 300). For example, thethree-dimensional model 10 of the patient's anatomy described above inconnection with FIG. 1 may be trimmed and discretized into a volumetricmesh, e.g., a finite element or finite volume mesh. The volumetric meshmay be used to generate the equations 30 described above in connectionwith FIG. 1.

Boundary conditions may also be assigned and incorporated into theequations 30 described above in connection with FIG. 1. The boundaryconditions provide information about the three-dimensional model 10 atits boundaries, e.g., the inflow boundaries 322 (FIG. 8), the outflowboundaries 324 (FIG. 8), the vessel wall boundaries 326 (FIG. 8), etc.The inflow boundaries 322 may include the boundaries through which flowis directed into the anatomy of the three-dimensional model, such as atan end of the aorta near the aortic root (e.g., end A shown in FIG. 16).Each inflow boundary 322 may be assigned, e.g., with a prescribed valueor field for velocity, flow rate, pressure, or other characteristic, bycoupling a heart model and/or a lumped parameter model to the boundary,etc. The outflow boundaries 324 may include the boundaries through whichflow is directed outward from the anatomy of the three-dimensionalmodel, such as at an end of the aorta near the aortic arch (e.g., end Bshown in FIG. 16), and the downstream ends of the main coronary arteriesand the branches that extend therefrom (e.g., ends a-m shown in FIG.16). Each outflow boundary can be assigned, e.g., by coupling a lumpedparameter or distributed (e.g., a one-dimensional wave propagation)model, as will be described in detail below. The prescribed values forthe inflow and/or outflow boundary conditions may be determined bynoninvasively measuring physiologic characteristics of the patient, suchas, but not limited to, cardiac output (the volume of blood flow fromthe heart), blood pressure, myocardial mass, etc. The vessel wallboundaries may include the physical boundaries of the aorta, the maincoronary arteries, and/or other coronary arteries or vessels of thethree-dimensional model 10.

The computational analysis may be performed using the preparedthree-dimensional model and the determined boundary conditions (step400) to determine blood flow information for the patient. For example,the computational analysis may be performed with the equations 30 andusing the computer 40 described above in connection with FIG. 1 toproduce the images described above in connection with FIG. 1, such asthe simulated blood pressure model 50, the simulated blood flow model52, and/or the cFFR model 54.

The method may also include providing patient-specific treatment optionsusing the results (step 500). For example, the three-dimensional model10 created in step 200 and/or the boundary conditions assigned in step300 may be adjusted to model one or more treatments, e.g., placing acoronary stent in one of the coronary arteries represented in thethree-dimensional model 10 or other treatment options. Then, thecomputational analysis may be performed as described above in step 400in order to produce new images, such as updated versions of the bloodpressure model 50, the blood flow model 52, and/or the cFFR model 54.These new images may be used to determine a change in blood flowvelocity and pressure if the treatment option(s) are adopted.

The systems and methods disclosed herein may be incorporated into asoftware tool accessed by physicians to provide a noninvasive means toquantify blood flow in the coronary arteries and to assess thefunctional significance of coronary artery disease. In addition,physicians may use the software tool to predict the effect of medical,interventional, and/or surgical treatments on coronary artery bloodflow. The software tool may prevent, diagnose, manage, and/or treatdisease in other portions of the cardiovascular system includingarteries of the neck (e.g., carotid arteries), arteries in the head(e.g., cerebral arteries), arteries in the thorax, arteries in theabdomen (e.g., the abdominal aorta and its branches), arteries in thearms, or arteries in the legs (e.g., the femoral and poplitealarteries). The software tool may be interactive to enable physicians todevelop optimal personalized therapies for patients.

For example, the software tool may be incorporated at least partiallyinto a computer system, e.g., the computer 40 shown in FIG. 1 used by aphysician or other user. The computer system may receive data obtainednoninvasively from the patient (e.g., data used to create thethree-dimensional model 10, data used to apply boundary conditions orperform the computational analysis, etc.). For example, the data may beinput by the physician or may be received from another source capable ofaccessing and providing such data, such as a radiology or other medicallab. The data may be transmitted via a network or other system forcommunicating the data, or directly into the computer system. Thesoftware tool may use the data to produce and display thethree-dimensional model 10 or other models/meshes and/or any simulationsor other results determined by solving the equations 30 described abovein connection with FIG. 1, such as the simulated blood pressure model50, the simulated blood flow model 52, and/or the cFFR model 54. Thus,the software tool may perform steps 100-500. In step 500, the physicianmay provide further inputs to the computer system to select possibletreatment options, and the computer system may display to the physiciannew simulations based on the selected possible treatment options.Further, each of steps 100-500 shown in FIG. 2 may be performed usingseparate software packages or modules.

Alternatively, the software tool may be provided as part of a web-basedservice or other service, e.g., a service provided by an entity that isseparate from the physician. The service provider may, for example,operate the web-based service and may provide a web portal or otherweb-based application (e.g., run on a server or other computer systemoperated by the service provider) that is accessible to physicians orother users via a network or other methods of communicating data betweencomputer systems. For example, the data obtained noninvasively from thepatient may be provided to the service provider, and the serviceprovider may use the data to produce the three-dimensional model 10 orother models/meshes and/or any simulations or other results determinedby solving the equations 30 described above in connection with FIG. 1,such as the simulated blood pressure model 50, the simulated blood flowmodel 52, and/or the cFFR model 54. Then, the web-based service maytransmit information relating to the three-dimensional model 10 or othermodels/meshes and/or the simulations so that the three-dimensional model10 and/or the simulations may be displayed to the physician on thephysician's computer system. Thus, the web-based service may performsteps 100-500 and any other steps described below for providingpatient-specific information. In step 500, the physician may providefurther inputs, e.g., to select possible treatment options or make otheradjustments to the computational analysis, and the inputs may betransmitted to the computer system operated by the service provider(e.g., via the web portal). The web-based service may produce newsimulations or other results based on the selected possible treatmentoptions, and may communicate information relating to the new simulationsback to the physician so that the new simulations may be displayed tothe physician.

One or more of the steps described herein may be performed by one ormore human operators (e.g., a cardiologist or other physician, thepatient, an employee of the service provider providing the web-basedservice or other service provided by a third party, other user, etc.),or one or more computer systems used by such human operator(s), such asa desktop or portable computer, a workstation, a server, a personaldigital assistant, etc. The computer system(s) may be connected via anetwork or other method of communicating data.

FIG. 3 shows further aspects of the exemplary method for providingvarious information relating to blood flow in a specific patient. Theaspects shown in FIG. 3 may be incorporated into the software tool thatmay be incorporated at least partially into a computer system and/or aspart of a web-based service.

II. Obtaining and Preprocessing Patient-Specific Anatomical Data

As described above in connection with step 100 shown in FIG. 2, theexemplary method may include obtaining patient-specific anatomical data,such as information regarding the patient's heart, and preprocessing thedata. In an exemplary embodiment, step 100 may include the followingsteps.

Initially, a patient may be selected. For example, the patient may beselected by the physician when the physician determines that informationabout the patient's coronary blood flow is desired, e.g., if the patientis experiencing symptoms associated with coronary artery disease, suchas chest pain, heart attack, etc.

Patient-specific anatomical data may be obtained, such as data regardingthe geometry of the patient's heart, e.g., at least a portion of thepatient's aorta, a proximal portion of the main coronary arteries (andthe branches extending therefrom) connected to the aorta, and themyocardium. The patient-specific anatomical data may be obtainednoninvasively, e.g., using a noninvasive imaging method. For example,CCTA is an imaging method in which a user may operate a computertomography (CT) scanner to view and create images of structures, e.g.,the myocardium, the aorta, the main coronary arteries, and other bloodvessels connected thereto. The CCTA data may be time-varying, e.g., toshow changes in vessel shape over a cardiac cycle. CCTA may be used toproduce an image of the patient's heart. For example, 64-slice CCTA datamay be obtained, e.g., data relating to 64 slices of the patient'sheart, and assembled into a three-dimensional image. FIG. 4 shows anexample of a three-dimensional image 120 produced by the 64-slice CCTAdata.

Alternatively, other noninvasive imaging methods, such as magneticresonance imaging (MRI) or ultrasound (US), or invasive imaging methods,such as digital subtraction angiography (DSA), may be used to produceimages of the structures of the patient's anatomy. The imaging methodsmay involve injecting the patient intravenously with a contrast agent toenable identification of the structures of the anatomy. The resultingimaging data (e.g., provided by CCTA, MRI, etc.) may be provided by athird-party vendor, such as a radiology lab or a cardiologist, by thepatient's physician, etc.

Other patient-specific anatomical data may also be determined from thepatient noninvasively. For example, physiological data such as thepatient's blood pressure, baseline heart rate, height, weight,hematocrit, stroke volume, etc., may be measured. The blood pressure maybe the blood pressure in the patient's brachial artery (e.g., using apressure cuff), such as the maximum (systolic) and minimum (diastolic)pressures.

The patient-specific anatomical data obtained as described above may betransferred over a secure communication line (e.g., via a network). Forexample, the data may be transferred to a server or other computersystem for performing the computational analysis, e.g., thecomputational analysis described above in step 400. In an exemplaryembodiment, the data may be transferred to a server or other computersystem operated by a service provider providing a web-based service.Alternatively, the data may be transferred to a computer system operatedby the patient's physician or other user.

Referring back to FIG. 3, the transferred data may be reviewed todetermine if the data is acceptable (step 102). The determination may beperformed by the user and/or by the computer system. For example, thetransferred data (e.g., the CCTA data and other data) may be verified bya user and/or by the computer system, e.g., to determine if the CCTAdata is complete (e.g., includes sufficient portions of the aorta andthe main coronary arteries) and corresponds to the correct patient.

The transferred data (e.g., the CCTA data and other data) may also bepreprocessed and assessed. The preprocessing and/or assessment may beperformed by a user and/or by the computer system and may include, e.g.,checking for misregistration, inconsistencies, or blurring in the CCTAdata, checking for stents shown in the CCTA data, checking for otherartifacts that may prevent the visibility of lumens of the bloodvessels, checking for sufficient contrast between the structures (e.g.,the aorta, the main coronary arteries, and other blood vessels) and theother portions of the patient, etc.

The transferred data may be evaluated to determine if the data isacceptable based on the verification, preprocessing, and/or assessmentdescribed above. During the verification, preprocessing, and/orassessment described above, the user and/or computer system may be ableto correct certain errors or problems with the data. If, however, thereare too many errors or problems, then the data may be determined to beunacceptable, and the user and/or computer system may generate arejection report explaining the errors or problems necessitating therejection of the transferred data. Optionally, a new CCTA scan may beperformed and/or the physiological data described above may be measuredfrom the patient again. If the transferred data is determined to beacceptable, then the method may proceed to step 202 described below.

Accordingly, step 102 shown in FIG. 3 and described above may beconsidered as a substep of step 100 of FIG. 2.

III. Creating the Three-Dimensional Model Based on Obtained AnatomicalData

As described above in connection with step 200 shown in FIG. 2, theexemplary method may include creating the three-dimensional model basedon the obtained anatomical data. In an exemplary embodiment, step 200may include the following steps.

Using the CCTA data, a three-dimensional model of the coronary vesselsmay be generated. FIG. 5 shows an example of the surface of athree-dimensional model 220 generated using the CCTA data. For example,the model 220 may include, e.g., at least a portion of the aorta, atleast a proximal portion of one or more main coronary arteries connectedto that portion of the aorta, at least a proximal portion of one or morebranches connected to the main coronary arteries, etc. The modeledportions of the aorta, the main coronary arteries, and/or the branchesmay be interconnected and treelike such that no portion is disconnectedfrom the rest of the model 220. The process of forming the model 220 iscalled segmentation.

Referring back to FIG. 3, the computer system may automatically segmentat least a portion of the aorta (step 202) and the myocardium (or otherheart tissue, or other tissue connected to the arteries to be modeled)(step 204). The computer system may also segment at least a portion ofthe main coronary arteries connected to the aorta. In an exemplaryembodiment, the computer system may allow the user to select one or morecoronary artery root or starting points (step 206) in order to segmentthe main coronary arteries.

Segmentation may be performed using various methods. Segmentation may beperformed automatically by the computer system based on user inputs orwithout user inputs. For example, in an exemplary embodiment, the usermay provide inputs to the computer system in order to generate a firstinitial model. For example, the computer system may display to the userthe three-dimensional image 120 (FIG. 4) or slices thereof produced fromthe CCTA data. The three-dimensional image 120 may include portions ofvarying intensity of lightness. For example, lighter areas may indicatethe lumens of the aorta, the main coronary arteries, and/or thebranches. Darker areas may indicate the myocardium and other tissue ofthe patient's heart.

FIG. 6 shows a portion of a slice 222 of the three-dimensional image 120that may be displayed to the user, and the slice 222 may include an area224 of relative lightness. The computer system may allow the user toselect the area 224 of relative lightness by adding one or more seeds226, and the seeds 226 may serve as coronary artery root or startingpoints for segmenting the main coronary arteries. At the command of theuser, the computer system may then use the seeds 226 as starting pointsto form the first initial model. The user may add seeds 226 in one ormore of the aorta and/or the individual main coronary arteries.Optionally, the user may also add seeds 226 in one or more of thebranches connected to the main coronary arteries. Alternatively, thecomputer system may place the seeds automatically, e.g., using extractedcenterline information. The computer system may determine an intensityvalue of the image 120 where the seeds 226 have been placed and may formthe first initial model by expanding the seeds 226 along the portions ofthe image 120 having the same intensity value (or within a range orthreshold of intensity values centered at the selected intensity value).Thus, this method of segmentation may be called “threshold-basedsegmentation.”

FIG. 7 shows a portion 230 of the first initial model that is formed byexpanding the seeds 226 of FIG. 6. Accordingly, the user inputs theseeds 226 as starting points for the computer system to begin formingthe first initial model. This process may be repeated until the entireportions of interest, e.g., the portions of the aorta and/or the maincoronary arteries, are segmented. Alternatively, the first initial modelmay be generated by the computer system without user inputs.

Alternatively, segmentation may be performed using a method called“edge-based segmentation.” In an exemplary embodiment, both thethreshold-based and edge-based segmentation methods may be performed, aswill be described below, to form the model 220.

A second initial model may be formed using the edge-based segmentationmethod. With this method, the lumen edges of the aorta and/or the maincoronary arteries may be located. For example, in an exemplaryembodiment, the user may provide inputs to the computer system, e.g.,the seeds 226 as described above, in order to generate the secondinitial model. The computer system may expand the seeds 226 along theportions of the image 120 until the edges are reached. The lumen edgesmay be located, e.g., by the user visually, and/or by the computersystem (e.g., at locations where there is a change in intensity valueabove a set threshold). The edge-based segmentation method may beperformed by the computer system and/or the user.

The myocardium or other tissue may also be segmented based on the CCTAdata in step 204. For example, the CCTA data may be analyzed todetermine the location of the internal and external surfaces of themyocardium, e.g., the left and/or right ventricles. The locations of thesurfaces may be determined based on the contrast (e.g., relativedarkness and lightness) of the myocardium compared to other structuresof the heart in the CCTA data. Thus, the geometry of the myocardium maybe determined.

The segmentation of the aorta, the myocardium, and/or the main coronaryarteries may be reviewed and/or corrected, if necessary (step 208). Thereview and/or correction may be performed by the computer system and/orthe user. For example, in an exemplary embodiment, the computer systemmay automatically review the segmentation, and the user may manuallycorrect the segmentation if there are any errors, e.g., if any portionsof the aorta, the myocardium, and/or the main coronary arteries in themodel 220 are missing or inaccurate.

For example, the first and second initial models described above may becompared to ensure that the segmentation of the aorta and/or the maincoronary arteries is accurate. Any areas of discrepancy between thefirst and second initial models may be compared to correct thesegmentation and to form the model 220. For example, the model 220 maybe an average between the first and second initial models.Alternatively, only one of the segmentation methods described above maybe performed, and the initial model formed by that method may be used asthe model 220.

The myocardial mass may be calculated (step 240). The calculation may beperformed by the computer system. For example, the myocardial volume maybe calculated based on the locations of the surfaces of the myocardiumdetermined as described above, and the calculated myocardial volume maybe multiplied by the density of the myocardium to calculate themyocardial mass. The density of the myocardium may be preset.

The centerlines of the various vessels (e.g., the aorta, the maincoronary arteries, etc.) of the model 220 (FIG. 5) may be determined(step 242). In an exemplary embodiment, the determination may beperformed automatically by the computer system.

The centerlines determined in step 242 may be reviewed and/or corrected,if necessary (step 244). The review and/or correction may be performedby the computer system and/or the user. For example, in an exemplaryembodiment, the computer system may automatically review thecenterlines, and the user may manually correct the centerlines if thereare any errors, e.g., if any centerlines are missing or inaccurate.

Calcium or plaque (causing narrowing of a vessel) may be detected (step246). In an exemplary embodiment, the computer system may automaticallydetect the plaque. For example, the plaque may be detected in thethree-dimensional image 120 and removed from the model 220. The plaquemay be identified in the three-dimensional image 120 since the plaqueappears as areas that are even lighter than the lumens of the aorta, themain coronary arteries, and/or the branches. Thus, the plaque may bedetected by the computer system as having an intensity value below a setvalue or may be detected visually by the user. After detecting theplaque, the computer system may remove the plaque from the model 220 sothat the plaque is not considered as part of the lumen or open space inthe vessels. Alternatively, the computer system may indicate the plaqueon the model 220 using a different color, shading, or other visualindicator than the aorta, the main coronary arteries, and/or thebranches.

The computer system may also automatically segment the detected plaque(step 248). For example, the plaque may be segmented based on the CCTAdata. The CCTA data may be analyzed to locate the plaque (or a surfacethereof) based on the contrast (e.g., relative darkness and lightness)of the plaque compared to other structures of the heart in the CCTAdata. Thus, the geometry of the plaque may also be determined.

The segmentation of the plaque may be reviewed and/or corrected, ifnecessary (step 250). The review and/or correction may be performed bythe computer system and/or the user. For example, in an exemplaryembodiment, the computer system may automatically review thesegmentation, and the user may manually correct the segmentation ifthere are any errors, e.g., if any plaque is missing or showninaccurately.

The computer system may automatically segment the branches connected tothe main coronary arteries (step 252). For example, the branches may besegmented using similar methods for segmenting the main coronaryarteries, e.g., as shown in FIGS. 6 and 7 and described above inconnection with step 206. The computer system may also automaticallysegment the plaque in the segmented branches using similar methods asdescribed above in connection with steps 248 and 250. Alternatively, thebranches (and any plaque contained therein) may be segmented at the sametime as the main coronary arteries (e.g., in step 206).

The segmentation of the branches may be reviewed and/or corrected, ifnecessary (step 254). The review and/or correction may be performed bythe computer system and/or the user. For example, in an exemplaryembodiment, the computer system may automatically review thesegmentation, and the user may manually correct the segmentation ifthere are any errors, e.g., if any portions of the branches in the model220 are missing or inaccurate.

The model 220 may be corrected if any misregistration, stents, or otherartifacts are located (e.g., during the review of the CCTA data in step102) (step 256). The correction may be performed by a user and/or by thecomputer system. For example, if a misregistration or other artifact(e.g., inconsistency, blurring, an artifact affecting lumen visibility,etc.) is located, the model 220 may be reviewed and/or corrected toavoid an artificial or false change in the cross-sectional area of avessel (e.g., an artificial narrowing). If a stent is located, the model220 may be reviewed and/or corrected to indicate the location of thestent and/or to correct the cross-sectional area of the vessel where thestent is located, e.g., based on the size of the stent.

The segmentation of the model 220 may also be independently reviewed(step 258). The review may be performed by a user and/or by the computersystem. For example, the user and/or computer system may be able toidentify certain errors with the model 220, such as correctable errorsand/or errors that may require the model 220 to be at least partiallyredone or resegmented. If such errors are identified, then thesegmentation may be determined to be unacceptable, and certain steps,e.g., one or more of steps 202-208, 240-256, depending on the error(s),may be repeated.

If the segmentation of the model 220 is independently verified asacceptable, then, optionally, the model 220 may be output and smoothed(step 260). The smoothing may be performed by the user and/or by thecomputer system. For example, ridges, points, or other discontinuousportions may be smoothed. The model 220 may be output to a separatesoftware module to be prepared for computational analysis, etc.

Accordingly, steps 202-208 and 240-260 shown in FIG. 3 and describedabove may be considered as substeps of step 200 of FIG. 2.

IV. Preparing the Model for Analysis and Determining Boundary Conditions

As described above in connection with step 300 shown in FIG. 2, theexemplary method may include preparing the model for analysis anddetermining boundary conditions. In an exemplary embodiment, step 300may include the following steps.

A. Preparing the Model For Analysis

Referring back to FIG. 3, the cross-sectional areas of the variousvessels (e.g., the aorta, the main coronary arteries, and/or thebranches) of the model 220 (FIG. 5) may also be determined (step 304).In an exemplary embodiment, the determination may be performed by thecomputer system.

The model 220 (FIG. 5) may be trimmed (step 306) and a solid model maybe generated. FIG. 8 shows an example of the trimmed solid model 320prepared based on a model similar to the model 220 shown in FIG. 5. Thesolid model 320 is a three-dimensional patient-specific geometric model.In an exemplary embodiment, the trimming may be performed by thecomputer system, with or without a user's input. Each of the inflowboundaries 322 and outflow boundaries 324 may be trimmed such that thesurface forming the respective boundary is perpendicular to thecenterlines determined in step 242. The inflow boundaries 322 mayinclude the boundaries through which flow is directed into the anatomyof the model 320, such as at an upstream end of the aorta, as shown inFIG. 8. The outflow boundaries 324 may include the boundaries throughwhich flow is directed outward from the anatomy of the model 320, suchas at a downstream end of the aorta and the downstream ends of the maincoronary arteries and/or branches.

B. Determining Boundary Conditions

Boundary conditions may be provided to describe what is occurring at theboundaries of the model, e.g., the three-dimensional solid model 320 ofFIG. 8. For example, the boundary conditions may relate to at least oneblood flow characteristic associated with the patient's modeled anatomy,e.g., at the boundaries of the modeled anatomy, and the blood flowcharacteristic(s) may include blood flow velocity, pressure, flow rate,FFR, etc. By appropriately determining the boundary conditions, acomputational analysis may be performed to determine information atvarious locations within the model. Examples of boundary conditions andmethods for determining such boundary conditions will now be described.

In an exemplary embodiment, the determined boundary conditions maysimplify the structures upstream and downstream from the portions of thevessels represented by the solid model 320 into a one- ortwo-dimensional reduced order model. An exemplary set of equations andother details for determining the boundary conditions are disclosed, forexample, in U.S. Patent Application Publication No. 2010/0241404 andU.S. Provisional Application No. 61/210,401, which are both entitled“Patient-Specific Hemodynamics of the Cardiovascular System” and herebyincorporated by reference in their entirety.

Boundary conditions may vary depending on the physiological condition ofthe patient since blood flow though the heart may differ depending onthe physiological condition of the patient. For example, FFR istypically measured under the physiological condition of hyperemia, whichgenerally occurs when the patient is experiencing increased blood flowin the heart, e.g., due to stress, etc. The FFR is the ratio of thecoronary pressure to aortic pressure under conditions of maximum stress.Hyperemia may also be induced pharmacologically, e.g., with adenosine.FIGS. 9-11 show examples of a calculated FFR (cFFR) model that indicatesthe change in the ratio of coronary pressure to aortic pressure in themodel 320, depending on the physiological condition of the patient (atrest, under maximum hyperemia, or under maximum exercise). FIG. 9 showsminimal variation in the ratio of coronary pressure to aortic pressurethroughout the model 320 when the patient is at rest. FIG. 10 showsgreater variation in the ratio of coronary pressure to aortic pressurethroughout the model 320 when the patient is undergoing maximumhyperemia. FIG. 11 shows even greater variation in the ratio of coronarypressure to aortic pressure throughout the model 320 when the patient isundergoing maximum exercise.

Referring back to FIG. 3, boundary conditions for hyperemia conditionsmay be determined (step 310). In an exemplary embodiment, the effect ofadenosine may be modeled using a decrease in coronary artery resistanceby a factor of 1-5 fold, a decrease in aortic blood pressure ofapproximately 0-20%, and an increase in heart rate of approximately0-20%. For example, the effect of adenosine may be modeled using adecrease in coronary artery resistance by a factor of 4 fold, a decreasein aortic blood pressure of approximately 10%, and an increase in heartrate of approximately 10%. Although the boundary conditions forhyperemia conditions are determined in the exemplary embodiment, it isunderstood that boundary conditions for other physiological states, suchas rest, varying degrees of hyperemia, varying degrees of exercise,exertion, stress, or other conditions, may be determined.

Boundary conditions provide information about the three-dimensionalsolid model 320 at its boundaries, e.g., the inflow boundaries 322, theoutflow boundaries 324, vessel wall boundaries 326, etc., as shown inFIG. 8. The vessel wall boundaries 326 may include the physicalboundaries of the aorta, the main coronary arteries, and/or othercoronary arteries or vessels of the model 320.

Each inflow or outflow boundary 322, 324 may be assigned a prescribedvalue or field of values for velocity, flow rate, pressure, or otherblood flow characteristic. Alternatively, each inflow or outflowboundary 322, 324 may be assigned by coupling a heart model to theboundary, a lumped parameter or distributed (e.g. one-dimensional wavepropagation) model, another type of one- or two-dimensional model, orother type of model. The specific boundary conditions may be determinedbased on, e.g., the geometry of the inflow or outflow boundaries 322,324 determined from the obtained patient-specific information, or othermeasured parameters, such as cardiac output, blood pressure, themyocardial mass calculated in step 240, etc.

i. Determining Reduced Order Models

The upstream and downstream structures connected to the solid model 320may be represented as reduced order models representing the upstream anddownstream structures. For example, FIGS. 12-15 show aspects of a methodfor preparing a lumped parameter model from three-dimensionalpatient-specific anatomical data at one of the outflow boundaries 324,according to an exemplary embodiment. The method may be performedseparately from and prior to the methods shown in FIGS. 2 and 3.

FIG. 12 shows a portion 330 of the solid model 320 of one of the maincoronary arteries or the branches extending therefrom, and FIG. 13 showsthe portion of the centerlines determined in step 242 of the portion 330shown in FIG. 12.

The portion 330 may be divided into segments 332. FIG. 14 shows anexample of the segments 332 that may be formed from the portion 330. Theselection of the lengths of the segments 332 may be performed by theuser and/or the computer system. The segments 332 may vary in length,depending, for example, on the geometry of the segments 332. Varioustechniques may be used to segment the portion 330. For example, diseasedportions, e.g., portions with a relatively narrow cross-section, alesion, and/or a stenosis (an abnormal narrowing in a blood vessel), maybe provided in one or more separate segments 332. The diseased portionsand stenoses may be identified, e.g., by measuring the cross-sectionalarea along the length of the centerline and calculating locally minimumcross-sectional areas.

The segments 332 may be approximated by a circuit diagram including oneor more (linear or nonlinear) resistors 334 and/or other circuitelements (e.g., capacitors, inductors, etc.). FIG. 15 shows an exampleof the segments 332 replaced by a series of linear and nonlinearresistors 334. The individual resistances of the resistors 334 may bedetermined, e.g., based on an estimated flow and/or pressure across thecorresponding segment 332.

The resistance may be constant, linear, or non-linear, e.g., dependingon the estimated flow rate through the corresponding segment 332. Formore complex geometries, such as a stenosis, the resistance may varywith flow rate. Resistances for various geometries may be determinedbased on a computational analysis (e.g., a finite difference, finitevolume, spectral, lattice Boltzmann, particle-based, level set,isogeometric, or finite element method, or other computational fluiddynamics (CFD) analytical technique), and multiple solutions from thecomputational analysis performed under different flow and pressureconditions may be used to derive patient-specific, vessel-specific,and/or lesion-specific resistances. The results may be used to determineresistances for various types of features and geometries of any segmentthat may be modeled. As a result, deriving patient-specific,vessel-specific, and/or lesion-specific resistances as described abovemay allow the computer system to recognize and evaluate more complexgeometry such as asymmetric stenosis, multiple lesions, lesions atbifurcations and branches and tortuous vessels, etc.

Capacitors may be also included, and capacitance may be determined,e.g., based on elasticity of the vessel walls of the correspondingsegment. Inductors may be included, and inductance may be determined,e.g., based on inertial effects related to acceleration or decelerationof the blood volume flowing through the corresponding segment.

The individual values for resistance, capacitance, inductance, and othervariables associated with other electrical components used in the lumpedparameter model may be derived based on data from many patients, andsimilar vessel geometries may have similar values. Thus, empiricalmodels may be developed from a large population of patient-specificdata, creating a library of values corresponding to specific geometricfeatures that may be applied to similar patients in future analyses.Geometries may be matched between two different vessel segments toautomatically select the values for a segment 332 of a patient from aprevious simulation.

ii. Exemplary Lumped Parameter Models

Alternatively, instead of performing the steps described above inconnection with FIGS. 12-15, the lumped parameter models may be preset.For example, FIG. 16 shows examples of lumped parameter models 340, 350,360 representing the upstream and downstream structures at the inflowand outflow boundaries 322, 324 of the solid model 320. End A is locatedat the inflow boundary 322, and ends a-m and B are located at theoutflow boundaries.

A lumped parameter heart model 340 may be used to determine the boundarycondition at the end A at the inflow boundary 322 of the solid model320. The lumped parameter heart model 340 may be used to represent bloodflow from the heart under hyperemia conditions. The lumped parameterheart model 340 includes various parameters (e.g., P_(LA), R_(AV),L_(AV), R_(V-Art), L_(V-Art), and E(t)) that may be determined based onknown information regarding the patient, e.g., an aortic pressure, thepatient's systolic and diastolic blood pressures (e.g., as determined instep 100), the patient's cardiac output (the volume of blood flow fromthe heart, e.g., calculated based on the patient's stroke volume andheart rate determined in step 100), and/or constants determinedexperimentally.

A lumped parameter coronary model 350 may be used to determine theboundary conditions at the ends a-m at the outflow boundaries 324 of thesolid model 320 located at the downstream ends of the main coronaryarteries and/or the branches that extend therefrom. The lumped parametercoronary model 350 may be used to represent blood flow exiting from themodeled vessels through the ends a-m under hyperemia conditions. Thelumped parameter coronary model 350 includes various parameters (e.g.,R_(a), C_(a), R_(a-micro), C_(im), and R_(v)) that may be determinedbased on known information regarding the patient, e.g., the calculatedmyocardial mass (e.g., as determined in step 240) and terminal impedanceat the ends a-m (e.g., determined based on the cross-sectional areas ofthe vessels at the ends a-m as determined in step 304).

For example, the calculated myocardial mass may be used to estimate abaseline (resting) mean coronary flow through the plurality of outflowboundaries 324. This relationship may be based on anexperimentally-derived physiological law (e.g., of the physiologicallaws 20 of FIG. 1) that correlates the mean coronary flow Q with themyocardial mass M (e.g., as determined in step 240) as Q∝Q_(o)M^(α),where α is a preset scaling exponent and Q_(o) is a preset constant. Thetotal coronary flow Q at the outflow boundaries 324 under baseline(resting) conditions and the patient's blood pressure (e.g., asdetermined in step 100) may then be used to determine a total resistanceR at the outflow boundaries 324 based on a preset,experimentally-derived equation.

The total resistance R may be distributed among the ends a-m based onthe respective cross-sectional areas of the ends a-m (e.g., asdetermined in step 304). This relationship may be based on anexperimentally-derived physiological law (e.g., of the physiologicallaws 20 of FIG. 1) that correlates the respective resistance at the endsa-m as R_(i)∝R_(i,o)d_(i) ^(β) where R_(i) is the resistance to flow atthe i-th outlet, and R_(o) is a preset constant, d_(i) is the diameterof that outlet, and β is a preset power law exponent, e.g., between −3and −2, −2.7 for coronary flow, −2.9 for cerebral flow, etc. Thecoronary flow through the individual ends a-m and the mean pressures atthe individual ends a-m (e.g., determined based on the individualcross-sectional areas of the ends a-m of the vessels as determined instep 304) may be used to determine a sum of the resistances of thelumped parameter coronary model 350 at the corresponding ends a-m (e.g.,R_(a)+R_(a-micro)+R_(v)). Other parameters (e.g., R_(a)/R_(a-micro),C_(a), C_(im)) may be constants determined experimentally.

A Windkessel model 360 may be used to determine the boundary conditionat the end B at the outflow boundary 324 of the solid model 320 locatedat the downstream end of the aorta toward the aortic arch. TheWindkessel model 360 may be used to represent blood flow exiting fromthe modeled aorta through the end B under hyperemia conditions. TheWindkessel model 360 includes various parameters (e.g., R_(p), R_(d),and C) that may be determined based on known information regarding thepatient, e.g., the patient's cardiac output described above inconnection with the lumped parameter heart model 340, the baseline meancoronary flow described above in connection with the lumped parametercoronary model 350, an aortic pressure (e.g., determined based on thecross-sectional area of the aorta at the end B as determined in step304), and/or constants determined experimentally.

The boundary conditions, e.g., the lumped parameter models 340, 350, 360(or any of the constants included therein) or other reduced order model,may be adjusted based on other factors. For example, resistance valuesmay be adjusted (e.g., increased) if a patient has a lower flow tovessel size ratio due to a comparatively diminished capacity to dilatevessels under physiologic stress. Resistance values may also be adjustedif the patient has diabetes, is under medication, has undergone pastcardiac events, etc.

Alternate lumped parameter or distributed, one-dimensional networkmodels may be used to represent the coronary vessels downstream of thesolid model 320. Myocardial perfusion imaging using MRI, CT, PET, orSPECT may be used to assign parameters for such models. Also, alternateimaging sources, e.g., magnetic resonance angiography (MRA),retrospective cine gating or prospective cine gating computed tomographyangiography (CTA), etc., may be used to assign parameters for suchmodels. Retrospective cine gating may be combined with image processingmethods to obtain ventricular chamber volume changes over the cardiaccycle to assign parameters to a lumped parameter heart model.

Simplifying a portion of the patient's anatomy using the lumpedparameter models 340, 350, 360, or other reduced order one- ortwo-dimensional model allows the computational analysis (e.g., step 402of FIG. 3 described below) to be performed more quickly, particularly ifthe computational analysis is performed multiple times such as whenevaluating possible treatment options (e.g., step 500 of FIG. 2) inaddition to the untreated state (e.g., step 400 of FIGS. 2 and 3), whilemaintaining high accuracy with the final results.

In an exemplary embodiment, the determination of the boundary conditionsmay be performed by the computer system based on the user's inputs, suchas patient-specific physiological data obtained in step 100.

C. Creating the Three-Dimensional Mesh

Referring back to FIG. 3, a three-dimensional mesh may be generatedbased on the solid model 320 generated in step 306 (step 312). FIGS.17-19 show an example of a three-dimensional mesh 380 prepared based onthe solid model 320 generated in step 306. The mesh 380 includes aplurality of nodes 382 (meshpoints or gridpoints) along the surfaces ofthe solid model 320 and throughout the interior of the solid model 320.The mesh 380 may be created with tetrahedral elements (having pointsthat form the nodes 382), as shown in FIGS. 18 and 19. Alternatively,elements having other shapes may be used, e.g., hexahedrons or otherpolyhedrons, curvilinear elements, etc. In an exemplary embodiment, thenumber of nodes 382 may be in the millions, e.g., five to fifty million.The number of nodes 382 increases as the mesh 380 becomes finer. With ahigher number of nodes 382, information may be provided at more pointswithin the model 320, but the computational analysis may take longer torun since a greater number of nodes 382 increases the number ofequations (e.g., the equations 30 shown in FIG. 1) to be solved. In anexemplary embodiment, the generation of the mesh 380 may be performed bythe computer system, with or without a user's input (e.g., specifying anumber of the nodes 382, the shapes of the elements, etc.).

Referring back to FIG. 3, the mesh 380 and the determined boundaryconditions may be verified (step 314). The verification may be performedby a user and/or by the computer system. For example, the user and/orcomputer system may be able to identify certain errors with the mesh 380and/or the boundary conditions that require the mesh 380 and/or theboundary conditions to be redone, e.g., if the mesh 380 is distorted ordoes not have sufficient spatial resolution, if the boundary conditionsare not sufficient to perform the computational analysis, if theresistances determined in step 310 appear to be incorrect, etc. If so,then the mesh 380 and/or the boundary conditions may be determined to beunacceptable, and one or more of steps 304-314 may be repeated. If themesh 380 and/or the boundary conditions are determined to be acceptable,then the method may proceed to step 402 described below.

In addition, the user may check that the obtained patient-specificinformation, or other measured parameters, such as cardiac output, bloodpressures, height, weight, the myocardial mass calculated in step 240,are entered correctly and/or calculated correctly.

Accordingly, steps 304-314 shown in FIG. 3 and described above may beconsidered as substeps of step 300 of FIG. 2.

V. Performing the Computational Analysis and Outputting Results

As described above in connection with step 400 shown in FIG. 2, theexemplary method may include performing the computational analysis andoutputting results. In an exemplary embodiment, step 400 may include thefollowing steps.

A. Performinq the Computational Analysis

Referring to FIG. 3, the computational analysis may be performed by thecomputer system (step 402). In an exemplary embodiment, step 402 maylast minutes to hours, depending, e.g., on the number of nodes 382 inthe mesh 380 (FIGS. 17-19), etc.

The analysis involves generating a series of equations that describe theblood flow in the model 320 from which the mesh 380 was generated. Asdescribed above, in the exemplary embodiment, the desired informationrelates to the simulation of blood flow through the model 320 underhyperemic conditions.

The analysis also involves using a numerical method to solve thethree-dimensional equations of blood flow using the computer system. Forexample, the numerical method may be a known method, such as finitedifference, finite volume, spectral, lattice Boltzmann, particle-based,level set, isogeometric, or finite element methods, or othercomputational fluid dynamics (CFD) numerical techniques.

Using these numerical methods, the blood may be modeled as a Newtonian,a non-Newtonian, or a multiphase fluid. The patient's hematocrit orother factors measured in step 100 may be used to determine bloodviscosity for incorporation in the analysis. The blood vessel walls maybe assumed to be rigid or compliant. In the latter case, equations forwall dynamics, e.g., the elastodynamics equations, may be solvedtogether with the equations for blood flow. Time-varyingthree-dimensional imaging data obtained in step 100 may be used as aninput to model changes in vessel shape over the cardiac cycle. Anexemplary set of equations and steps for performing the computationalanalysis are disclosed in further detail, for example, in U.S. Pat. No.6,236,878, which is entitled “Method for Predictive Modeling forPlanning Medical Interventions and Simulating Physiological Conditions,”and U.S. Patent Application Publication No. 2010/0241404 and U.S.Provisional Application No. 61/210,401, which are both entitled“Patient-Specific Hemodynamics of the Cardiovascular System,” all ofwhich are hereby incorporated by reference in their entirety.

The computational analysis using the prepared model and boundaryconditions may determine blood flow and pressure at each of the nodes382 of the mesh 380 representing the three-dimensional solid model 320.For example, the results of the computational analysis may includevalues for various parameters at each of the nodes 382, such as, but notlimited to, various blood flow characteristics or parameters, such asblood flow velocity, pressure, flow rate, or computed parameters, suchas cFFR, as described below. The parameters may also be interpolatedacross the three-dimensional solid model 320. As a result, the resultsof the computational analysis may provide the user with information thattypically may be determined invasively.

Referring back to FIG. 3, the results of the computational analysis maybe verified (step 404). The verification may be performed by a userand/or by the computer system. For example, the user and/or computersystem may be able to identify certain errors with the results thatrequire the mesh 380 and/or the boundary conditions to be redone orrevised, e.g., if there is insufficient information due to aninsufficient number of nodes 382, if the analysis is taking too long dueto an excessive number of nodes 382, etc.

If the results of the computational analysis are determined to beunacceptable in step 404, then the user and/or computer system maydetermine, for example, whether and how to revise or refine the solidmodel 320 generated in step 306 and/or the mesh 380 generated in step312, whether and how to revise the boundary conditions determined instep 310, or whether to make other revisions to any of the inputs forthe computational analysis. Then, one or more steps described above,e.g., steps 306-314, 402, and 404 may be repeated based on thedetermined revisions or refinements.

B. Displaying Results for Blood Pressure, Flow, and oFFR

Referring back to FIG. 3, if the results of the computational analysisare determined to be acceptable in step 404, then the computer systemmay output certain results of the computational analysis. For example,the computer system may display images generated based on the results ofthe computational analysis, such as the images described above inconnection with FIG. 1, such as the simulated blood pressure model 50,the simulated blood flow model 52, and/or the cFFR model 54. As notedabove, these images indicate the simulated blood pressure, blood flow,and cFFR under simulated hyperemia conditions, e.g., since the boundaryconditions determined in step 310 were determined with respect tohyperemia conditions.

The simulated blood pressure model 50 (FIG. 1) shows the local bloodpressure (e.g., in millimeters of mercury or mmHg) throughout thepatient's anatomy represented by the mesh 380 of FIGS. 17-19 undersimulated hyperemia conditions. The computational analysis may determinethe local blood pressure at each node 382 of the mesh 380, and thesimulated blood pressure model 50 may assign a corresponding color,shade, or other visual indicator to the respective pressures such thatthe simulated blood pressure model 50 may visually indicate thevariations in pressure throughout the model 50 without having to specifythe individual values for each node 382. For example, the simulatedblood pressure model 50 shown in FIG. 1 shows that, for this particularpatient, under simulated hyperemia conditions, the pressure may begenerally uniform and higher in the aorta (as indicated by the darkershading), and that the pressure gradually and continuously decreases asthe blood flows downstream into the main coronary arteries and into thebranches (as shown by the gradual and continuous lightening in shadingtoward the downstream ends of the branches). The simulated bloodpressure model 50 may be accompanied by a scale indicating the specificnumerical values for blood pressure, as shown in FIG. 1.

In an exemplary embodiment, the simulated blood pressure model 50 may beprovided in color, and a color spectrum may be used to indicatevariations in pressure throughout the model 50. The color spectrum mayinclude red, orange, yellow, green, blue, indigo, and violet, in orderfrom highest pressure to lowest pressure. For example, the upper limit(red) may indicate approximately 110 mmHg or more (or 80 mmHg, 90 mmHg,100 mmHg, etc.), and the lower limit (violet) may indicate approximately50 mmHg or less (or 20 mmHg, 30 mmHg, 40 mmHg, etc.), with greenindicating approximately 80 mmHg (or other value approximately halfwaybetween the upper and lower limits). Thus, the simulated blood pressuremodel 50 for some patients may show a majority or all of the aorta asred or other color towards the higher end of the spectrum, and thecolors may change gradually through the spectrum (e.g., towards thelower end of the spectrum (down to violet)) towards the distal ends ofthe coronary arteries and the branches that extend therefrom. The distalends of the coronary arteries for a particular patient may havedifferent colors, e.g., anywhere from red to violet, depending on thelocal blood pressures determined for the respective distal ends.

The simulated blood flow model 52 (FIG. 1) shows the local bloodvelocity (e.g., in centimeters per second or cm/s) throughout thepatient's anatomy represented by the mesh 380 of FIGS. 17-19 undersimulated hyperemia conditions. The computational analysis may determinethe local blood velocity at each node 382 of the mesh 380, and thesimulated blood flow model 52 may assign a corresponding color, shade,or other visual indicator to the respective velocities such that thesimulated blood flow model 52 may visually indicate the variations invelocity throughout the model 52 without having to specify theindividual values for each node 382. For example, the simulated bloodflow model 52 shown in FIG. 1 shows that, for this particular patient,under simulated hyperemia conditions, the velocity is generally higherin certain areas of the main coronary arteries and the branches (asindicated by the darker shading in area 53 in FIG. 1). The simulatedblood flow model 52 may be accompanied by a scale indicating thespecific numerical values for blood velocity, as shown in FIG. 1.

In an exemplary embodiment, the simulated blood flow model 52 may beprovided in color, and a color spectrum may be used to indicatevariations in velocity throughout the model 52. The color spectrum mayinclude red, orange, yellow, green, blue, indigo, and violet, in orderfrom highest velocity to lowest velocity. For example, the upper limit(red) may indicate approximately 100 (or 150) cm/s or more, and thelower limit (violet) may indicate approximately 0 cm/s, with greenindicating approximately 50 cm/s (or other value approximately halfwaybetween the upper and lower limits). Thus, the simulated blood flowmodel 52 for some patients may show a majority or all of the aorta as amixture of colors towards the lower end of the spectrum (e.g., greenthrough violet), and the colors may change gradually through thespectrum (e.g., towards the higher end of the spectrum (up to red)) atcertain locations where the determined blood velocities increase.

The cFFR model 54 (FIG. 1) shows the local cFFR throughout the patient'sanatomy represented by the mesh 380 of FIGS. 17-19 under simulatedhyperemia conditions. As noted above, cFFR may be calculated as theratio of the local blood pressure determined by the computationalanalysis (e.g., shown in the simulated blood pressure model 50) at aparticular node 382 divided by the blood pressure in the aorta, e.g., atthe inflow boundary 322 (FIG. 8). The computational analysis maydetermine the cFFR at each node 382 of the mesh 380, and the cFFR model54 may assign a corresponding color, shade, or other visual indicator tothe respective cFFR values such that the cFFR model 54 may visuallyindicate the variations in cFFR throughout the model 54 without havingto specify the individual values for each node 382. For example, thecFFR model 54 shown in FIG. 1 shows that, for this particular patient,under simulated hyperemia conditions, cFFR may be generally uniform andapproximately 1.0 in the aorta, and that cFFR gradually and continuouslydecreases as the blood flows downstream into the main coronary arteriesand into the branches. The cFFR model 54 may also indicate cFFR valuesat certain points throughout the cFFR model 54, as shown in FIG. 1. ThecFFR model 54 may be accompanied by a scale indicating the specificnumerical values for cFFR, as shown in FIG. 1.

In an exemplary embodiment, the cFFR model 54 may be provided in color,and a color spectrum may be used to indicate variations in pressurethroughout the model 54. The color spectrum may include red, orange,yellow, green, blue, indigo, and violet, in order from lowest cFFR(indicating functionally significant lesions) to highest cFFR. Forexample, the upper limit (violet) may indicate a cFFR of 1.0, and thelower limit (red) may indicate approximately 0.7 (or 0.75 or 0.8) orless, with green indicating approximately 0.85 (or other valueapproximately halfway between the upper and lower limits). For example,the lower limit may be determined based on a lower limit (e.g., 0.7,0.75, or 0.8) used for determining whether the cFFR measurementindicates a functionally significant lesion or other feature that mayrequire intervention. Thus, the cFFR model 54 for some patients may showa majority or all of the aorta as violet or other color towards thehigher end of the spectrum, and the colors may change gradually throughthe spectrum (e.g., towards the higher end of the spectrum (up toanywhere from red to violet) towards the distal ends of the coronaryarteries and the branches that extend therefrom. The distal ends of thecoronary arteries for a particular patient may have different colors,e.g., anywhere from red to violet, depending on the local values of cFFRdetermined for the respective distal ends.

After determining that the cFFR has dropped below the lower limit usedfor determining the presence of a functionally significant lesion orother feature that may require intervention, the artery or branch may beassessed to locate the functionally significant lesion(s). The computersystem or the user may locate the functionally significant lesion(s)based on the geometry of the artery or branch (e.g., using the cFFRmodel 54). For example, the functionally significant lesion(s) may belocated by finding a narrowing or stenosis located near (e.g., upstream)from the location of the cFFR model 54 having the local minimum cFFRvalue. The computer system may indicate or display to the user theportion(s) of the cFFR model 54 (or other model) that includes thefunctionally significant lesion(s).

Other images may also be generated based on the results of thecomputational analysis. For example, the computer system may provideadditional information regarding particular main coronary arteries,e.g., as shown in FIGS. 20-22. The coronary artery may be chosen by thecomputer system, for example, if the particular coronary artery includesthe lowest cFFR. Alternatively, the user may select the particularcoronary artery.

FIG. 20 shows a model of the patient's anatomy including results of thecomputational analysis with certain points on the model identified byindividual reference labels (e.g., LM, LAD1, LAD2, LAD3, etc.). In theexemplary embodiment shown in FIG. 21, the points are provided in theLAD artery, which is the main coronary artery having the lowest cFFR forthis particular patient, under simulated hyperemia conditions.

FIGS. 21 and 22 show graphs of certain variables over time at some orall of these points (e.g., LM, LAD1, LAD2, LAD3, etc.) and/or at certainother locations on the model (e.g., in the aorta, etc.). FIG. 21 is agraph of the pressure (e.g., in millimeters of mercury or mmHg) overtime in the aorta and at points LAD1, LAD2, and LAD3 indicated in FIG.20. The top plot on the graph indicates the pressure in the aorta, thesecond plot from the top indicates the pressure at point LAD1, the thirdplot from the top indicates the pressure at point LAD2, and the bottomplot indicates the pressure at point LAD3. FIG. 22 is a graph of theflow (e.g., in cubic centimeters per second or cc/s) over time at pointsLM, LAD1, LAD2, and LAD3 indicated in FIG. 20. In addition, other graphsmay be provided, such as a graph of shear stress over time at some orall of these points and/or at other points. The top plot on the graphindicates the flow at point LM, the second plot from the top indicatesthe flow at point LAD1, the third plot from the top indicates the flowat point LAD2, and the bottom plot indicates the flow at point LAD3.Graphs may also be provided that show the change in these variables,e.g., blood pressure, flow, velocity, or cFFR, along the length of aparticular main coronary artery and/or the branches extending therefrom.

Optionally, the various graphs and other results described above may befinalized in a report (step 406). For example, the images and otherinformation described above may be inserted into a document having a settemplate. The template may be preset and generic for multiple patients,and may be used for reporting the results of computational analyses tophysicians and/or patients. The document or report may be automaticallycompleted by the computer system after the computational analysis iscompleted.

For example, the finalized report may include the information shown inFIG. 23. FIG. 23 includes the cFFR model 54 of FIG. 1 and also includessummary information, such as the lowest cFFR values in each of the maincoronary arteries and the branches that extend therefrom. For example,FIG. 23 indicates that the lowest cFFR value in the LAD artery is 0.66,the lowest cFFR value in the LCX artery is 0.72, the lowest cFFR valuein the RCA artery is 0.80. Other summary information may include thepatient's name, the patient's age, the patient's blood pressure (BP)(e.g., obtained in step 100), the patient's heart rate (HR) (e.g.,obtained in step 100), etc. The finalized report may also includeversions of the images and other information generated as describedabove that the physician or other user may access to determine furtherinformation. The images generated by the computer system may beformatted to allow the physician or other user to position a cursor overany point to determine the value of any of the variables describedabove, e.g., blood pressure, velocity, flow, cFFR, etc., at that point.

The finalized report may be transmitted to the physician and/or thepatient. The finalized report may be transmitted using any known methodof communication, e.g., a wireless or wired network, by mail, etc.Alternatively, the physician and/or patient may be notified that thefinalized report is available for download or pick-up. Then, thephysician and/or patient may log into the web-based service to downloadthe finalized report via a secure communication line.

C. Verifying Results

Referring back to FIG. 3, the results of the computational analysis maybe independently verified (step 408). For example, the user and/orcomputer system may be able to identify certain errors with the resultsof the computational analysis, e.g., the images and other informationgenerated in step 406, that require any of the above described steps tobe redone. If such errors are identified, then the results of thecomputational analysis may be determined to be unacceptable, and certainsteps, e.g., steps 100, 200, 300, 400, substeps 102, 202-208, 240-260,304-314, and 402-408, etc., may be repeated.

Accordingly, steps 402-408 shown in FIG. 3 and described above may beconsidered as substeps of step 400 of FIG. 2.

Another method for verifying the results of the computational analysismay include measuring any of the variables included in the results,e.g., blood pressure, velocity, flow, cFFR, etc., from the patient usinganother method. In an exemplary embodiment, the variables may bemeasured (e.g., invasively) and then compared to the results determinedby the computational analysis. For example, FFR may be determined, e.g.,using a pressure wire inserted into the patient as described above, atone or more points within the patient's anatomy represented by the solidmodel 320 and the mesh 380. The measured FFR at a location may becompared with the cFFR at the same location, and the comparison may beperformed at multiple locations. Optionally, the computational analysisand/or boundary conditions may be adjusted based on the comparison.

VI. Providing Patient-Specific Treatment Planning

As described above in connection with step 500 shown in FIG. 2, theexemplary method may include providing patient-specific treatmentplanning. In an exemplary embodiment, step 500 may include the followingsteps. Although FIG. 3 does not show the following steps, it isunderstood that these steps may be performed in conjunction with thesteps shown in FIG. 3, e.g., after steps 406 or 408. Moreover, asdescribed above, any of the following described sub-steps of step 500may be performed by a computing system, such as computer 40, and/or byone or more computing systems, servers systems, and/or web servers.

As described above, the cFFR model 54 shown in FIGS. 1 and 23 indicatesthe cFFR values throughout the patient's anatomy represented by the mesh380 of FIGS. 17-19 in an untreated state and under simulated hyperemiaconditions. Using this information, the physician may prescribetreatments to the patient, such as an increase in exercise, a change indiet, a prescription of medication, surgery on any portion of themodeled anatomy or other portions of the heart (e.g., coronary arterybypass grafting, insertion of one or more coronary stents, etc.), etc.

To determine which treatment(s) to prescribe, the computer system may beused to predict how the information determined from the computationalanalysis would change based on such treatment(s). For example, certaintreatments, such as insertion of stent(s) or other surgeries, may resultin a change in geometry of the modeled anatomy. Accordingly, in anexemplary embodiment, the solid model 320 generated in step 306 may berevised to indicate a widening of one or more lumens where a stent isinserted.

For example, the cFFR model 54 shown in FIGS. 1 and 23 indicates thatthe lowest cFFR value in the LAD artery is 0.66, the lowest cFFR valuein the LCX artery is 0.72, the lowest cFFR value in the RCA artery is0.80. Treatment may be proposed if a cFFR value is, for example, lessthan 0.75. Accordingly, the computer system may propose to the userrevising the solid model 320 to indicate a widening of the LAD arteryand the LCX artery to simulate inserting stents in these coronaryarteries. The user may be prompted to choose the location and amount ofwidening (e.g., the length and diameter) corresponding to the locationand size of the simulated stent. Alternatively, the location and amountof widening may be determined automatically by the computer system basedon various factors, such as the location of the node(s) with cFFR valuesthat are less than 0.75, a location of a significant narrowing of thevessels, sizes of conventional stents, etc.

FIG. 25 shows an example of a modified cFFR model 510 determined basedon a solid model created by widening a portion of the LAD artery atlocation 512 and a portion of the LCX artery at location 514. In anexemplary embodiment, any of the steps described above, e.g., steps310-314 and 402-408, may be repeated using the modified solid model. Instep 406, the finalized report may include the information relating tothe untreated patient (e.g., without the stents), such as theinformation shown in FIG. 23, and information relating to the simulatedtreatment for the patient, such as the information shown in FIGS. 25 and26.

FIG. 25 includes the modified cFFR model 510 and also includes summaryinformation, such as the lowest cFFR values in the main coronaryarteries and the branches that extend therefrom for the modified solidmodel associated with the proposed treatment. For example, FIG. 25indicates that the lowest cFFR value in the LAD artery (and itsdownstream branches) is 0.78, the lowest cFFR value in the LCX artery(and its downstream branches) is 0.78, the lowest cFFR value in the RCAartery (and its downstream branches) is 0.79. Accordingly, a comparisonof the cFFR model 54 of the untreated patient (without stents) and thecFFR model 510 for the proposed treatment (with stents inserted)indicates that the proposed treatment may increase the minimum cFFR inthe LAD artery from 0.66 to 0.78 and would increase the minimum cFFR inthe LCX artery from 0.72 to 0.76, while there would be a minimaldecrease in the minimum cFFR in the RCA artery from 0.80 to 0.79.

FIG. 26 shows an example of a modified simulated blood flow model 520determined after widening portions of the LAD artery at location 512 andof the LCX artery at location 514 as described above. FIG. 26 alsoincludes summary information, such as the blood flow values at variouslocations in the main coronary arteries and the branches that extendtherefrom for the modified solid model associated with the proposedtreatment. For example, FIG. 26 indicates blood flow values for fourlocations LAD1, LAD2, LAD3, and LAD4 in the LAD artery and for twolocations LCX1 and LCX2 in the LCX artery for the untreated patient(without stents) and for the treated patient (with stents inserted).FIG. 26 also indicates a percentage change in blood flow values betweenthe untreated and treated states. Accordingly, a comparison of thesimulated blood flow model 52 of the untreated patient and the simulatedblood flow model 520 for the proposed treatment indicates that theproposed treatment may increase the flow through the LAD artery and LCXartery at all of the locations LAD1-LAD4, LCX1, and LCX2 by 9% to 19%,depending on the location.

Other information may also be compared between the untreated and treatedstates, such as coronary artery blood pressure. Based on thisinformation, the physician may discuss with the patient whether toproceed with the proposed treatment option.

Other treatment options may also involve modifying the solid model 320in different ways. For example, coronary artery bypass grafting mayinvolve creating new lumens or passageways in the solid model 320 andremoving a lesion may also involve widening a lumen or passage. Othertreatment options may not involve modifying the solid model 320. Forexample, an increase in exercise or exertion, a change in diet or otherlifestyle change, a prescription of medication, etc., may involvechanging the boundary conditions determined in step 310, e.g., due tovasoconstriction, dilation, decreased heart rate, etc. For example, thepatient's heart rate, cardiac output, stroke volume, blood pressure,coronary microcirculation function, the configurations of the lumpedparameter models, etc., may depend on the medication prescribed, thetype and frequency of exercise adopted (or other exertion), the type oflifestyle change adopted (e.g., cessation of smoking, changes in diet,etc.), thereby affecting the boundary conditions determined in step 310in different ways.

In an exemplary embodiment, modified boundary conditions may bedetermined experimentally using data from many patients, and similartreatment options may require modifying the boundary conditions insimilar ways. Empirical models may be developed from a large populationof patient-specific data, creating a library of boundary conditions orfunctions for calculating boundary conditions, corresponding to specifictreatment options that may be applied to similar patients in futureanalyses.

After modifying the boundary conditions, the steps described above,e.g., steps 312, 314, and 402-408, may be repeated using the modifiedboundary conditions, and in step 406, the finalized report may includethe information relating to the untreated patient, such as theinformation shown in FIG. 23, and information relating to the simulatedtreatment for the patient, such as the information shown in FIGS. 25 and26.

Alternatively, the physician, the patient, or other user may be providedwith a user interface that allows interaction with a three-dimensionalmodel (e.g., the solid model 320 of FIG. 8). The model 320 may bedivided into user-selectable segments that may be edited by the user toreflect one or more treatment options. For example, the user may selecta segment with a stenosis (or occlusion, e.g., an acute occlusion) andadjust the segment to remove the stenosis, the user may add a segment tothe model 320 to serve as a bypass, etc. The user may also be promptedto specify other treatment options and/or physiologic parameters thatmay alter the boundary conditions determined above, e.g., a change in acardiac output, a heart rate, a stroke volume, a blood pressure, anexercise or exertion level, a hyperemia level, medications, etc. In analternate embodiment, the computer system may determine or suggest atreatment option.

The user interface may allow interaction with the three-dimensionalmodel 320 to allow the user to simulate a stenosis (or occlusion, e.g.,an acute occlusion). For example, the user may select a segment forincluding the stenosis, and the computer system may be used to predicthow the information determined from the computational analysis wouldchange based on the addition of the stenosis. Thus, the methodsdescribed herein may be used to predict the effect of occluding anartery.

The user interface may also allow interaction with the three-dimensionalmodel 320 to simulate a damaged artery or removal of an artery, whichmay occur, for example, in certain surgical procedures, such as whenremoving cancerous tumors. The model may also be modified to simulatethe effect of preventing blood flow through certain arteries in order topredict the potential for collateral pathways for supplying adequateblood flow for the patient.

A. Using Reduced Order Models to Compare Different Treatment Options

In an exemplary embodiment, the computer system may allow the user tosimulate various treatment options more quickly by replacing thethree-dimensional solid model 320 or mesh 380 with a reduced ordermodel. FIG. 27 shows a schematic diagram relating to a method 700 forsimulating various treatment options using a reduced order model,according to an exemplary embodiment. The method 700 may be implementedin the computer system described above.

One or more patient-specific simulated blood flow models representingblood flow or other parameters may be output from the computationalanalysis described above (step 701). For example, the simulated bloodflow models may include the simulated blood pressure model 50 of FIG. 1,the simulated blood flow model 52 of FIG. 1, the cFFR model 54 of FIG.1, etc., provided using the methods described above and shown in FIGS. 2and 3. As described above, the simulated blood flow model may include athree-dimensional geometrical model of the patient's anatomy.

Functional information may be extracted from the simulated blood flowmodels in order to specify conditions for a reduced order model (step702). For example, the functional information may include the bloodpressure, flow, or velocity information determined using thecomputational analysis described above.

A reduced order (e.g., zero-dimensional or one-dimensional) model may beprovided to replace the three-dimensional solid model 320 used togenerate the patient specific simulated blood flow models generated instep 701, and the reduced order model may be used to determineinformation about the coronary blood flow in the patient (step 703). Forexample, the reduced order model may be a lumped parameter modelgenerated as described above in connection with step 310 of FIG. 3.Thus, the lumped parameter model is a simplified model of the patient'sanatomy that may be used to determine information about the coronaryblood flow in the patient without having to solve the more complexsystem of equations associated with the mesh 380 of FIGS. 17-19.

Information determined from solving the reduced order model in step 703may then be mapped or extrapolated to a three-dimensional solid model(e.g., the solid model 320) of the patient's anatomy (step 704), and theuser may make changes to the reduced order model as desired to simulatevarious treatment options and/or changes to the physiologic parametersfor the patient, which may be selected by the user (step 705). Theselectable physiologic parameters may include cardiac output, exerciseor exertion level, level of hyperemia, types of medications, etc. Theselectable treatment options may include removing a stenosis, adding abypass, etc.

Then, the reduced order model may be modified based on the treatmentoptions and/or physiologic parameters selected by the user, and themodified reduced order model may be used to determine information aboutthe coronary blood flow in the patient associated with the selectedtreatment option and/or physiologic parameter (step 703). Informationdetermined from solving the reduced order model in step 703 may then bemapped or extrapolated to the three-dimensional solid model 320 of thepatient's anatomy to predict the effects of the selected treatmentoption and/or physiologic parameter on the coronary blood flow in thepatient's anatomy (step 704).

Steps 703-705 may be repeated for various different treatment optionsand/or physiologic parameters to compare the predicted effects ofvarious treatment options to each other and to the information about thecoronary blood flow in the untreated patient. As a result, predictedresults for various treatment options and/or physiologic parameters maybe evaluated against each other and against information about theuntreated patient without having to rerun the more complex analysisusing the three-dimensional mesh 380. Instead, a reduced order model maybe used, which may allow the user to analyze and compare differenttreatment options and/or physiologic parameters more easily and quickly.

FIG. 28 shows further aspects of the exemplary method for simulatingvarious treatment options using a reduced order model, according to anexemplary embodiment. The method 700 may be implemented in the computersystem described above.

As described above in connection with step 306 of FIG. 3, apatient-specific geometric model may be generated based on imaging datafor the patient (step 711). For example, the imaging data may includethe CCTA data obtained in step 100 of FIG. 2, and the geometric modelmay be the solid model 320 of FIG. 8 generated in step 306 of FIG. 3,and/or the mesh 380 of FIGS. 17-19 generated in step 312 of FIG. 3.

Using the patient-specific three-dimensional geometric model, thecomputational analysis may be performed, e.g., as described above inconnection with step 402 of FIG. 3, to determine information about thepatient's coronary blood flow (step 712). The computational analysis mayoutput one or more three-dimensional patient-specific simulated bloodflow models representing blood flow or other parameters, e.g., thesimulated blood pressure model 50 of FIG. 1, the simulated blood flowmodel 52 of FIG. 1, the cFFR model 54 of FIG. 1, etc.

The simulated blood flow model may be segmented (e.g., as describedabove in connection with FIG. 14) based on the anatomical features ofthe model (step 713). For example, branches extending from the maincoronary arteries may be provided in separate segments (step 714),portions with stenosis or diseased areas may be provided in separatesegments (step 716), and portions between the branches and the portionswith stenosis or diseased areas may be provided in separate segments(step 715). Varying degrees of resolution may be provided in segmentingthe simulated blood flow model such that each vessel may include aplurality of short, discrete segments or longer segments, e.g.,including the entire vessel. Also, various techniques may be providedfor segmenting the simulated blood flow model, including generatingcenterlines and sectioning based on the generated centerlines, ordetecting branch points and sectioning based on the detected branchpoints. The diseased portions and stenoses may be identified, e.g., bymeasuring the cross-sectional area along the length of the centerlineand calculating locally minimum cross-sectional areas. Steps 711-716 maybe considered as substeps of step 701 of FIG. 27.

The segments may be replaced by components of a lumped parameter model,such as resistors, capacitors, inductors, etc., as described above inconnection with FIG. 15. The individual values for the resistance,capacitance, inductance, and other variables associated with otherelectrical components used in the lumped parameter model may be derivedfrom the simulated blood flow models provided in step 712. For example,for branches and portions between the branches and the portions withstenosis or diseased areas, information derived from the simulated bloodflow model may be used to assign linear resistances to the correspondingsegments (step 717). For portions with complex geometry, such as astenosis or diseased area, resistance may vary with flow rate. Thus,multiple computational analyses may be used to obtain simulated bloodflow models for various flow and pressure conditions to derivepatient-specific, vessel-specific, and lesion-specific resistancefunctions for these complex geometries, as described above in connectionwith FIG. 15. Accordingly, for portions with stenosis or diseased areas,information derived from these multiple computational analyses or modelsderived from previous data may be used to assign non-linear,flow-dependent resistances to corresponding segments (step 718). Steps717 and 718 may be considered as substeps of step 702 of FIG. 27.

Using the resistances determined in steps 717 and 718, a reduced order(e.g., zero-dimensional or one-dimensional) model may be generated (step719). For example, the reduced order model may be a lumped parametermodel generated as described above in connection with step 310 of FIG.3. Thus, the lumped parameter model is a simplified model of thepatient's anatomy that may be used to determine information about thecoronary blood flow in the patient without having to solve the morecomplex system of equations associated with the mesh 380 of FIGS. 17-19.

A user interface may be provided that allows the user to interact withthe reduced order model created in step 719 (step 720). For example, theuser may select and edit different segments of the reduced order modelto simulate different treatment options and/or may edit variousphysiologic parameters. For example, intervention, such as insertion ofa stent to repair of a diseased region, may be modeled by decreasing theresistance of the segment where the stent is to be inserted. Forming abypass may be modeled by adding a segment having a low resistanceparallel to a diseased segment.

The modified reduced order model may be solved to determine informationabout the coronary blood flow in the patient under the treatment and/orchange in physiologic parameters selected in step 720 (step 721). Thesolution values for flow and pressure in each segment determined in step721 may then be compared to the three-dimensional solution determined instep 712, and any difference may be minimized by adjusting theresistance functions of the segments (e.g., as determined in steps 717and 718) and resolving the reduced order model (e.g., step 721) untilthe solutions match. As a result, the reduced order model may be createdand then solved with a simplified set of equations that allows forrelatively rapid computation (e.g., compared to a full three-dimensionalmodel) and may be used to solve for flow rate and pressure that mayclosely approximate the results of a full three-dimensionalcomputational solution. The reduced order model allows for relativelyrapid iterations to model various different treatment options.

Information determined from solving the reduced order model in step 721may then be mapped or extrapolated to a three-dimensional solid model ofthe patient's anatomy (e.g., the solid model 320) (step 722). Steps719-722 may be similar to steps 703-705 of FIG. 27 and may be repeatedas desired by the user to simulate different combinations of treatmentoptions and/or physiologic parameters.

Alternatively, rather than calculating the resistance along segmentsfrom the three-dimensional model (e.g., as described above for steps 717and 718), flow and pressure at intervals along the centerline may beprescribed into a lumped parameter or one-dimensional model. Theeffective resistances or loss coefficients may be solved for under theconstraints of the boundary conditions and prescribed flow and pressure.

Also, the flow rates and pressure gradients across individual segmentsmay be used to compute an epicardial coronary resistance using thesolution derived from the reduced-order model (e.g., as described abovefor step 721). The epicardial coronary resistance may be calculated asan equivalent resistance of the epicardial coronary arteries (theportions of the coronary arteries and the branches that extend therefromincluded in the patient-specific model reconstructed from medicalimaging data). This may have clinical significance in explaining whypatients with diffuse atherosclerosis in the coronary arteries mayexhibit symptoms of ischemia (restriction in blood supply). Also, theflow per unit of myocardial tissue volume (or mass) and/or the flow perunit of cardiac work under conditions of simulatedpharmacologically-induced hyperemia or varying exercise intensity may becalculated using data from the reduced-order models.

B. Modifying Patient-Specific Geometrical Models to Optimize TreatmentOptions

In addition to previously-described techniques for enabling a user torevise geometry in solid model 320 to widen lumens, and enabling a userto modify a reduced order model based on various treatment options,other embodiments of systems and methods are now disclosed forautomatically evaluating treatment options by modifying patient-specificgeometric models. For example, as described above, a cardiologist mayreview a three-dimensional patient specific geometrical model, anddecide to make changes to the model to reflect a treatment option thatthe cardiologist believes may provide better blood flow properties. Inaddition, a cardiologist may operate a computer system to update areduced-order model based on the changes that the cardiologist makes tothe geometrical model, to calculate whether the cardiologist's beliefabout improved blood flow properties is correct.

However, additional embodiments are now described for automaticallyevaluating treatment options by modifying patient-specific geometricmodels. For example, a computer system may automatically modifypatient-specific geometric models and evaluate treatment options, evenfor treatment options that a cardiologist does not necessarily know willimprove blood flow properties. Moreover, a computer may automaticallymodify patient-specific geometric models, hundreds or even thousands oftimes to reflect hundreds or even thousands of different possibletreatment options. For example, the computer system may automaticallymodel numerous different possible positions and types of bypass graftand/or stent interventions, model a patient's coronary geometry based onimplementation of those numerous types of interventions, and thenautomatically identify one or more suitable or desirable interventionsby automatically analyzing the models, e.g., using reduced ordermodeling. As will be described in more detail below, any type ofcomputing system, such as computer 40 (FIG. 1), may be used to processand evaluate patient-specific imaging data according to the exemplarymethod of FIG. 29.

FIG. 29 depicts a method 800 for automatically evaluating treatmentoptions by modifying patient-specific geometric models. As depicted,method 800 may include generating a patient-specific geometric modelfrom image data and physiological information (step 802). For example,the imaging data may include the CCTA data obtained in step 100 of FIG.2, and the formed geometric model may be the solid model 320 of FIG. 8generated in step 306 of FIG. 3, and/or the mesh 380 of FIGS. 17-19generated in step 312 of FIG. 3.

Method 800 may then include segmenting the simulated blood flow model(e.g., as described above in connection with FIG. 14) based on theanatomical features of the model, and creating a reduced-order modelbased on the patient-specific geometric model (step 804). First, varioustechniques may be provided for segmenting the simulated blood flowmodel, including generating centerlines and sectioning based on thegenerated centerlines, or detecting branch points and sectioning basedon the detected branch points. The diseased portions and stenoses may beidentified, e.g., by measuring the cross-sectional area along the lengthof the centerline and calculating locally minimum cross-sectional areas.The segments may be replaced by components of a lumped parameter model,such as resistors, capacitors, inductors, etc., as described above inconnection with FIG. 15. The individual values for the resistance,capacitance, inductance, and other variables associated with otherelectrical components used in the lumped parameter model may be derivedfrom the simulated blood flow models. For example, for branches andportions between the branches and the portions with stenosis or diseasedareas, information derived from the simulated blood flow model may beused to assign linear resistances to the corresponding segments.

A reduced order (e.g., zero-dimensional or one-dimensional) model maythen be generated using the determined resistances. For example, thereduced order model may be a lumped parameter model generated asdescribed above in connection with step 310 of FIG. 3. Thus, the lumpedparameter model is a simplified model of the patient's anatomy that maybe used to determine information about the coronary blood flow in thepatient without having to solve the more complex system of equationsassociated with the mesh 380 of FIGS. 17-19.

The modified reduced order model may be solved to determine informationabout the coronary blood flow in the patient (step 806). For example,using the patient-specific three-dimensional geometric model,computational analysis may be performed, e.g., as described above inconnection with step 402 of FIG. 3, to determine information about thepatient's coronary blood flow. The computational analysis may output oneor more three-dimensional patient-specific simulated blood flow modelsrepresenting blood flow or other parameters, e.g., the simulated bloodpressure model 50 of FIG. 1, the simulated blood flow model 52 of FIG.1, the cFFR model 54 of FIG. 1, etc. Thus, multiple computationalanalyses may be used to obtain simulated blood flow models for variousflow and pressure conditions to derive patient-specific,vessel-specific, and lesion-specific resistance functions for thesecomplex geometries, as described above in connection with FIG. 15.

Meanwhile, method 800 may also involve implementing geometricmodification techniques for modifying the generated patient-specificgeometric model to reflect a plurality of treatment options (step 808).Any suitable computerized modeling or computerized-aided draftingtechnique may be used for modifying a mesh associated with apatient-specific geometric model. For example, in one embodiment, ageometric domain modification technique may be used to perform aconstructive solid geometry (CSG) union for combining treated andoriginal patient arterial geometry. In another embodiment, an elasticdeformation modification technique may be used to deform a mesh model oforiginal patient arterial geometry to the shape of proposed treatedarterial geometry. Exemplary embodiments of geometric domainmodification and elastic deformation modification techniques will bedescribed in more detail below.

Method 800 may further include using one or more modification techniquesto model all possible treatment options (step 810). For example,modification techniques may simulate the insertion of a stent in allpossible locations of a patient's arterial trees. Modificationtechniques may simulate the insertion of all possible stents, includingall combinations of radii and lengths of stents, and/or all commerciallyavailable stents, based on a database of known commercial stentgeometries. Moreover, geometric modification techniques may simulate theinsertion of a plurality of stents, in any suitable locations. Forexample, given a patient's arterial tree having a plurality of arterialbranches, modification techniques may be used to identify every locationalong each arterial branch where a stent may be positioned. Moreover,the possible locations may be overlapping, such that a patient'sgeometric model is modified for a shift in stent location that issignificantly shorter than the stent itself. Likewise, modificationtechniques may be applied for all possible locations of a bypass graft,and all possible sizes and orientations of bypass grafts. The computersystem may also apply modification techniques for any possiblecombination of PCI and/or CABG interventions.

In one embodiment, the computing system may generate the set of possibletreatment options for every single feasible location within a patient'scoronary vasculature. In another embodiment, the computing system maygenerate the set of possible treatment options for sections of apatient's coronary vasculature having a predetermined threshold level ofenergy losses, or some other flow characteristic. For example, uponsolving for a patient's coronary blood flow characteristics in step 806,a computing system may identify those segments having a predeterminedblood flow characteristic, such as an FFR value below 0.75, or an FFRvalue that drops by more than 5% between arterial segments. Thecomputing system may then generate a set of potential treatment optionsfor those segments, using the geometric modification techniquesdescribed above, for all feasible types, sizes, and orientations ofvarious stents and/or bypass grafts.

Given a set of all possible treatment options, method 800 may includeperforming an iterative solving of the reduced order model for alltreatment options, using estimated parameters of the reduced order modelthat correspond to each treatment option (steps 812, 806). Specifically,the reduced order model may be efficiently executed for each possibletreatment option. In one embodiment, the reduced order model may be anetwork of resistors that represent the intrinsic resistances of athree-dimensional computational fluid dynamic model. The intrinsicresistances may be calculated by selecting endpoints of resistivesegments, determining pressures at those nodes, and flow throughsegments connecting these nodes, e.g., using pre-operative resultssolved for in step 806, and calculating resistances using Ohm's law. Thereduced order model may be coupled to resistances defined as boundaryconditions of the patient-specific geometry model.

In order to solve the reduced order model for each possible treatmentoption, estimated parameters associated with the possible treatmentoption may be used to modify the reduced order model. For example, inthe case of a resistor model, a resistance value estimated for a stentmay be inserted into the reduced order model at a suitable location forthe stent. The resistance value estimated for the stent may be moved toany of a plurality of suitable locations for the stent, and the reducedorder model may be solved for each possible location. As described abovewith respect to FIGS. 12-16, the reduced order model generated for eachpossible treatment option may be quickly solved using, for example,Ohm's law, Kirchhoff's current law, and/or Kirchhoff's voltage law.

In one embodiment, resistance values used in solving the reduced ordermodel for each treatment option, may be estimated based on an analyticalsolution for fully-developed flow in a circular cylinder (i.e., asPoiseuille flow). For example, for a given stent or bypass, it may beassumed that fully-developed flow exists across the length and diameterof the known dimensions and geometry of the possible stent or bypass.The computer system may then analytically solve for a resistance valueassociated with such flow. As an alternative to such an analyticaltechnique, resistance values associated with possible stent or bypassoptions may be obtained from historical data, such as a database orlibrary of known resistance values associated with various knowndimensions and geometries of previously implemented stents or bypassgrafts. Thus, a reduced order model may be created and solved for eachpossible treatment option, using a resistance value calculated,estimated, or otherwise predicted to be associated with the type andlocation of the respective possible treatment option. Moreover, thereduced order model may be created and then solved with a simplified setof equations that allows for relatively rapid computation (e.g.,compared to a full three-dimensional model) and may be used to solve forflow rate and pressure that may closely approximate the results of afull three-dimensional computational solution, given the respectivetreatment option. The reduced order model allows for relatively rapiditerations to model various different treatment options.

Method 800 may also include generating one or more objective functionsof blood flow characteristics solved from the plurality of reduced ordermodels (step 814). A suitable objective function may be a cost function,or any other multi-variable function that optimizes one or morevariables, relative to one or more other variables. In one embodiment, agenerated objective function may optimize one or more of the flowcharacteristics solved from the plurality of reduced order modelscorresponding to the plurality of treatment options. For example, theobjective function may be designed to identify one or more treatmentoptions that maximizes arterial flow, or minimizes FFR losses. In oneembodiment, the objective function may be designed to identify one ormore treatment options that optimize a Syntax score, as described inU.S. application Ser. No. 13/656,183 for Systems and Methods forNumerically Evaluating Vasculature, filed by Timothy A. Fonte et al. onOct. 19, 2012, the entire contents of which is incorporated herein byreference. The objective function may be designed to maximize flow,minimize pressure changes, or optimize any other desired characteristicof blood flow. Thus, solving the objective function may enableidentification of one or more of the treatment options (i.e., stentselection/location and/or bypass graft selection/location) thatoptimizes the desired characteristic. Because the objective functionoperates on results of the numerous reduced order models solved in steps806, 812, the objective function may quickly and automatically evaluatethe results of hundreds, thousands, or even tens of thousands ofdifferent treatment options.

In addition, the objective function may be configured to penalizecertain undesirable characteristics of possible treatment options.Specifically, the objective function may be designed such that anoptimum identified treatment is not necessarily the treatment with theabsolute highest maximized or lowest minimized variable, e.g., becauseit may have one or more penalties. For example, the objective functionmay be designed to apply penalties to treatment options having more thanone stent, and greater penalties with rising numbers of interventions(i.e., penalizing combinations of stents and bypass grafts). In oneembodiment, the objective function may penalize one or more of:increasing numbers of stents and/or bypass grafts; decreasing of FFRvalues in larger vessels, smaller vessels; increasing proximity of(i.e., decreasing distance between) inserted stents; and the existenceor number of bifurcations.

In one embodiment, the objective function may penalize certain treatmentoptions based on actual and/or estimated monetary costs of the one ormore treatment options. For example, the objective function may receiveor access a library of known hospital fees, physician fees, medicaldevice prices, insurance reimbursements, or any other monetary costsassociated with different treatments. The costs may be known to varybased on various patient factors, geography of the procedure, the typeof implanted medical device, the hospital or physician associated withthe procedure, a complexity of a surgical procedure, and so on. Thus,for example, as complexity increases, or numbers of stents or bypassesincreases, the projected or modeled costs of the treatment option mayalso increase, and the relevant treatment option may be penalizedaccordingly by the objective function.

In other words, the objective function may be designed to favortreatment options that are simple, e.g., using one stent or one bypass,and effective, e.g. resulting in significant outcomes for large vesselsover smaller vessels, even if those treatment options do not result inthe absolute most optimized blood flow characteristic. Such objectivefunctions may result in the identification of one or more locally orglobally optimized blood flow characteristics (step 816).

In one embodiment, when the objective function identifies a treatmentoption that optimizes a desired flow parameter (e.g., a global optimumthat minimizes FFR, maximizes flow, etc.), method 800 may includeoutputting that treatment option (step 818), such as by displaying theidentified treatment option. For example, method 800 may includedisplaying a patient-specific geometrical model as modified by theselected treatment option (e.g., stent or bypass graft). In addition, oralternatively, method 800 may include displaying a written or textualdescription of the selected treatment option. For example, method 800may include displaying the type, location, and/or orientation of thestent and/or bypass graft that optimizes the objective function.

In one embodiment, when the objective function identifies a localoptimum, such as an FFR value, pressure value, or flow value that isrelatively optimal, but not necessarily the most optimal value, method800 may optionally include modifying the surface mesh of thepatient-specific model based on the iterated treatment option thatresults in a local optimum (step 820). Thus, a locally optimum treatmentoption may be used to refine or create a new reduced order model bymodifying the patient-specific geometric model with the treatment optionusing one or more geometric modification techniques described withrespect to step 808. Such a technique may facilitate efficient andautomatic generation of revised surface meshes and reduced order modelsthat are most likely to result in identifying an optimum treatmentoption. Of course, a treatment option identified by modifying a surfacemesh based on iterated treatment option (step 820) and creating acorresponding reduced order model (step 804) may be output to a display,in relation to the patient-specific geometric model, three-dimensionalflow model, and/or FFRct model (step 818).

As described above with respect to step 808, a plurality of differenttechniques may be implemented for modifying a patient-specific geometricmodel, both for generating a set of all possible treatment options, andfor refining a surface mesh for generating a refined reduced order modelof blood flow. FIG. 30 depicts a method 850 of a geometric domainmodification technique for modifying a patient-specific geometric model.In general, geometric domain modification may involve augmenting avessel diameter by performing a CSG union of a patient's original vesselgeometry with a constructed geometry that represents a stented region.

In one embodiment, implicit functions may be used to construct thegeometry of a stented region. As shown in FIG. 30, method 850 mayinclude defining a plurality of spheres along discrete points of avessel to be treated (step 852). For example, a sphere centered at thepoint [c_(x), c_(y), c_(z)] with radius r may be described by theimplicit function (x−c_(x))²+(y−c_(y))²+(z−c_(z))²=r². Thus, havingdefined a sequential number of discrete points along a vessel, every twoconsecutive points (p_(n), p_(n+1)) along the path may be used to definea capsule.

Method 850 may then include performing a union of the defined spheres togenerate at least one capsule (step 854). Specifically, as reflected inthe diagram of FIG. 31A, each capsule may be defined as the union of thetwo spheres of specified radii at each point and the cone between themthat linearly interpolates the two radii.

Method 850 may then include identifying a plurality of CSG grid pointswithin the union of the at least one capsule (step 856). Specifically, acomputing system may construct a uniform CSG grid of adequate spacialresolution around the one or more capsules generated in step 854. FIG.31B depicts one embodiment of a plurality of CSG grid points around aunion forming a capsule. In one embodiment, for each grid point, asigned distance may be computed for each capsule, and the minimum valueover all of the capsules may be stored at each grid point. In oneembodiment, each signed distance may be the distance from a grid pointto the closest point on a capsule, where, as shown in FIG. 31B, apositive sign may indicate the point lies outside the surface and anegative sign indicates the point lies inside the surface. Thus, step856 may result in a grid of values that represent a union of allcapsules generated in step 854.

Method 850 may further include constructing a mesh of the proposedstented region from the CSG grid points generated in step 856 (step858). For example, any suitable CSG technique, including Marching-Cubesor Dual-Contouring may be used to extract an explicit triangle mesh fromthe CSG grid, thereby representing a section of the vessel that contoursto a proposed stent. FIG. 32 depicts a graphical representation of atriangle mesh of a proposed stent geometry, created by running aMarching-Cubes technique on a union of implicitly generated capsules.

Method 850 may further include performing a CSG union between the meshof the proposed stented region (as formed in step 858), and the mesh ofthe original patient geometry (step 860). FIG. 33A depicts a graphicalrepresentation of a triangle mesh of an original patient geometry havinga stenosis portion that appears as a visible narrowing of a vessel. FIG.33B depicts a graphical representation of a triangle mesh resulting froma CSG union between the original patient geometry mesh depicted in FIG.33A and the stent mesh geometry depicted in FIG. 32. In other words, thegeometrical mesh depicted in FIG. 33B reflects a merging or combining ofthe stent geometry generated in FIG. 32 and the stenosed geometrygenerated in FIG. 33A.

In addition to the geometric domain modification techniques describedabove with respect to FIGS. 30-33B, an elastic deformation modificationtechnique may also or alternatively be used for modifying apatient-specific geometric model. FIG. 34 depicts an exemplary method880 for performing an elastic deformation technique for modifying apatient-specific geometric model. In general, method 880 may involvedeforming a surface mesh of a patient-specific geometric model around anexplicit or implicit shape that represents a shape of a desiredtreatment option, such as a stent or bypass graft.

In one embodiment, method 880 may include obtaining a surface mesh ofpatient geometry to be deformed (step 882). For example, a surface meshmay be segmented for a section of an arterial vessel into which a stentmay be inserted, and opened using finite element software, or any typeof elastic deformation simulator. Method 880 may include settingmaterial properties of the tissue to be deformed (step 884), andassigning those material properties to the surface mesh. For example,the material properties may define the realistic elasticity, etc. ofactual vasculature tissue. Method 880 may then include applying knownstent geometry to a desired collision geometry (step 886). For example,for any of the set of possible treatment options, including any suitablestent types, geometries, or sizes, method 880 may include inserting oneor more geometric representations of such stents into the elasticdeformation simulator as a collision geometry. Method 880 may theninclude executing the finite element or elastic deformation simulator topush the surface mesh of a patient's original tissue geometry toapproach the surface of the inserted collision geometry (step 888). Inone embodiment, the surface mesh geometry may be refined as desired tocapture the effects of the collision while performing collisiondetection and response to avoid allowing surface geometry fromself-intersecting.

While the present disclosure describes embodiments of geometric domainmodification and elastic deformation modification, it will beappreciated that any suitable type of computerized graphics or otherconstructive solid geometry techniques may be used to modify models ofpatient geometry, for purposes of automatically identifying all possiblesets of treatment options, and evaluating those identified treatmentoptions.

As a result of the foregoing techniques, the accuracy ofthree-dimensional blood flow modeling may be combined with thecomputational simplicity and relative speed inherent in one-dimensionaland lumped parameter modeling technologies. Three-dimensionalcomputational methods may be used to numerically derive patient-specificone-dimensional or lumped parameter models that embednumerically-derived empirical models for pressure losses over normalsegments, stenoses, junctions, and other anatomical features. Improveddiagnosis for patients with cardiovascular disease may be provided, andplanning of medical, interventional, and surgical treatments may beperformed faster.

Also, the accuracy of three-dimensional computational fluid dynamicstechnologies may be combined with the computational simplicity andperformance capabilities of lumped parameter and one-dimensional modelsof blood flow. A three-dimensional geometric and physiologic model maybe decomposed automatically into a reduced-order one-dimensional orlumped parameter model. The three-dimensional model may be used tocompute the linear or nonlinear hemodynamic effects of blood flowthrough normal segments, stenoses, and/or branches, and to set theparameters of empirical models. The one-dimensional or lumped parametermodels may more efficiently and rapidly solve for blood flow andpressure in a patient-specific model, and display the results of thelumped parameter or one-dimensional solutions.

The reduced order patient-specific anatomic and physiologic model may beused to determine the effect of different medications or lifestylechanges (e.g., cessation of smoking, changes in diet, or increasedphysical activity) that alters heart rate, stroke volume, bloodpressure, or coronary microcirculatory function on coronary artery bloodflow. Such information may be used to optimize medical therapy or avertpotentially dangerous consequences of medications. The reduced ordermodel may also be used to determine the effect on coronary artery bloodflow of alternate forms and/or varying levels of physical activity orrisk of exposure to potential extrinsic force, e.g., when playingfootball, during space flight, when scuba diving, during airplaneflights, etc. Such information may be used to identify the types andlevel of physical activity that may be safe and efficacious for aspecific patient. The reduced order model may also be used to predict apotential benefit of percutaneous coronary interventions on coronaryartery blood flow in order to select the optimal interventionalstrategy, and/or to predict a potential benefit of coronary arterybypass grafting on coronary artery blood flow in order to select theoptimal surgical strategy.

The reduced order model may also be used to illustrate potentialdeleterious effects of an increase in the burden of arterial disease oncoronary artery blood flow and to predict, using mechanistic orphenomenological disease progression models or empirical data, whenadvancing disease may result in a compromise of blood flow to the heartmuscle. Such information may enable the determination of a “warrantyperiod” in which a patient observed to be initially free fromhemodynamically significant disease using noninvasive imaging may not beexpected to require medical, interventional, or surgical therapy, oralternatively, the rate at which progression might occur if adversefactors are continued.

The reduced order model may also be used to illustrate potentialbeneficial effects on coronary artery blood flow resulting from adecrease in the burden of coronary artery disease and to predict, usingmechanistic or phenomenological disease progression models or empiricaldata, when regression of disease may result in increased blood flowthrough the coronary arteries to the heart muscle. Such information maybe used to guide medical management programs including, but not limitedto, changes in diet, increased physical activity, prescription ofstatins or other medications, etc.

The reduced order model may also be incorporated into an angiographysystem to allow for live computation of treatment options while aphysician examines a patient in a cardiac catheterization lab. The modelmay be registered to the same orientation as the angiography display,allowing side-by-side or overlapping results of a live angiographic viewof the coronary arteries with simulated blood flow solutions. Thephysician may plan and alter treatment plans as observations are madeduring procedures, allowing for relatively rapid feedback before medicaldecisions are made. The physician may take pressure, FFR, or blood flowmeasurements invasively, and the measurements may be utilized to furtherrefine the model before predictive simulations are performed.

The reduced order model may also be incorporated into a medical imagingsystem or workstation. If derived from a library of previouspatient-specific simulation results, then the reduced order models maybe used in conjunction with geometric segmentation algorithms torelatively rapidly solve for blood flow information after completing animaging scan.

The reduced order model may also be used to model the effectiveness ofnew medical therapies or the cost/benefit of treatment options on largepopulations of patients. A database of multiple patient-specific lumpedparameter models (e.g., hundreds, thousands, or more) may provide modelsto solve in relatively short amounts of time. Relatively quick iterationand optimization may be provided for drug, therapy, or clinical trialsimulation or design. Adapting the models to represent treatments,patient responses to drugs, or surgical interventions may allowestimates of effectiveness to be obtained without the need to performpossibly costly and potentially risky large-scale clinical trials.

Any aspect set forth in any embodiment may be used with any otherembodiment set forth herein. Every device and apparatus set forth hereinmay be used in any suitable medical procedure, may be advanced throughany suitable body lumen and body cavity, and may be used for imaging anysuitable body portion.

Various modifications and variations can be made in the disclosedsystems and processes without departing from the scope of thedisclosure. Other embodiments will be apparent to those skilled in theart from consideration of the specification and practice of thedisclosure disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope and spiritof the disclosure being indicated by the following claims.

1-28. (canceled)
 29. A system for modifying a three-dimensional modelbased on one or more cardiovascular treatment options for a patient, thesystem comprising: at least one computer system configured for: creatinga three-dimensional model representing at least a portion of thepatient's heart or vasculature based on patient-specific data regardinga geometry of the patient's heart or vasculature; determining a geometryassociated with at least one of a plurality of treatment options fortreating at least a portion of the patient's heart or vasculature; anddetermining a modification of the three-dimensional model for at leastone of the plurality of treatment options, wherein the modification isbased on the geometry associated with the at least one of the pluralityof treatment options.
 30. The system of claim 29, wherein the computersystem is configured for: determining one or more modificationtechniques for making the modification, wherein the one or moremodification techniques are used to model the geometry associated withthe at least one of the plurality of treatment options, by simulating achange in the patient's heart or vasculature.
 31. The system of claim29, wherein the computer system is configured for: determining anoriginal patient arterial geometry based on the three-dimensional model;and determining a proposed treated arterial geometry associated with theat least one of the plurality of treatment options, wherein the proposedtreated arterial geometry is based, at least in part, on the geometryassociated with the at least one of the plurality of treatment options,wherein the modification of the three-dimensional model of thethree-dimensional model is based on the original patient arterialgeometry, the proposed treated arterial geometry, or a combinationthereof.
 32. The system of claim 29, wherein the computer system isconfigured for: identifying one or more locations in the threedimensional model where one or more stents, one or more grafts, or acombination thereof may be positioned, wherein the modification of thethree-dimensional model is based on the one or more locations.
 33. Thesystem of claim 32, wherein the computer system is configured for:determining, of the one or more locations, one or more overlappingregions, wherein the modification of the three-dimensional model isbased, at least in part, on the one or more overlapping regions.
 34. Thesystem of claim 32, wherein the computer system is configured for:determining at least one threshold level of an energy loss; andidentifying the one or more locations based on the at least onethreshold level of an energy loss.
 35. The system of claim 34, whereinthe computer system is configured for: determining one or more sectionsof the three-dimensional model based on the at least one threshold levelof an energy loss, wherein the modification of the three-dimensionalmodel is based, at least in part, on the one or more sections.
 36. Thesystem of claim 35, wherein the plurality of treatment options includesa set of possible treatment options for each of the one or moresections.
 37. A computer-implemented method for modifying athree-dimensional model based on one or more cardiovascular treatmentoptions for a patient, the method comprising: creating athree-dimensional model representing at least a portion of the patient'sheart or vasculature based on patient-specific data regarding a geometryof the patient's heart or vasculature; determining a geometry associatedwith at least one of a plurality of treatment options for treating atleast a portion of the patient's heart or vasculature; and determining amodification of the three-dimensional model for at least one of theplurality of treatment options, wherein the modification is based on thegeometry associated with the at least one of the plurality of treatmentoptions.
 38. The computer-implemented method of claim 37, furthercomprising: determining one or more modification techniques for makingthe modification, wherein the one or more modification techniques areused to model the geometry associated with the at least one of theplurality of treatment options, by simulating a change in the patient'sheart or vasculature.
 39. The computer-implemented method of claim 37,further comprising: determining an original patient arterial geometrybased on the three-dimensional model; and determining a proposed treatedarterial geometry associated with the at least one of the plurality oftreatment options, wherein the proposed treated arterial geometry isbased, at least in part, on the geometry associated with the at leastone of the plurality of treatment options, wherein the modification ofthe three-dimensional model of the three-dimensional model is based onthe original patient arterial geometry, the proposed treated arterialgeometry, or a combination thereof.
 40. The computer-implemented methodof claim 37, further comprising: identifying one or more locations inthe three dimensional model where one or more stents, one or moregrafts, or a combination thereof may be positioned, wherein themodification of the three-dimensional model is based on the one or morelocations.
 41. The computer-implemented method of claim 40, furthercomprising: determining, of the one or more locations, one or moreoverlapping regions, wherein the modification of the three-dimensionalmodel is based, at least in part, on the one or more overlappingregions.
 42. The computer-implemented method of claim 40, furthercomprising: determining at least one threshold level of an energy loss;and identifying the one or more locations based on the at least onethreshold level of an energy loss.
 43. The computer-implemented methodof claim 42, further comprising: determine one or more sections of thethree-dimensional model associated with the one or more locations,wherein the modification of the three-dimensional model is based, atleast in part, on the one or more sections.
 44. The computer-implementedmethod of claim 43, wherein the plurality of treatment options includesa set of possible treatment options for each of the one or moresections.
 45. A non-transitory computer readable medium for use on acomputer system containing computer-executable programming instructionsfor modifying a three-dimensional model based on one or morecardiovascular treatment options for a patient, the method comprising: aprocessor configured to execute the instructions to perform a methodincluding: creating a three-dimensional model representing at least aportion of the patient's heart or vasculature based on patient-specificdata regarding a geometry of the patient's heart or vasculature;determining a geometry associated with at least one of a plurality oftreatment options for treating at least a portion of the patient's heartor vasculature; and determining a modification of the three-dimensionalmodel for at least one of the plurality of treatment options, whereinthe modification is based on the geometry associated with the at leastone of the plurality of treatment options.
 46. The non-transitorycomputer readable medium of claim 45, the method further comprising:determining one or more modification techniques for making themodification, wherein the one or more modification techniques are usedto model the geometry associated with the at least one of the pluralityof treatment options, by simulating a change in the patient's heart orvasculature.
 47. The non-transitory computer readable medium of claim45, the method further comprising: determining an original patientarterial geometry based on the three-dimensional model; and determininga proposed treated arterial geometry associated with the at least one ofthe plurality of treatment options, wherein the proposed treatedarterial geometry is based, at least in part, on the geometry associatedwith the at least one of the plurality of treatment options, wherein themodification of the three-dimensional model of the three-dimensionalmodel is based on the original patient arterial geometry, the proposedtreated arterial geometry, or a combination thereof.
 48. Thenon-transitory computer readable medium of claim 17, the method furthercomprising: identifying one or more locations in the three dimensionalmodel where one or more stents, one or more grafts, or a combinationthereof may be positioned, wherein the modification of thethree-dimensional model is based on the one or more locations.